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Klimyk, Anatoliy Ul’yanovich

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Author ID: klimyk.anatoliy-u Recent zbMATH articles by "Klimyk, Anatoliy Ul’yanovich"
Published as: Klimyk, A. U.; Klimyk, Anatoli U.; Klimyk, Anatoliy U.; Klimyk, Anatoliy; Klimyk, A.; Klimyk, Anatoli
External Links: Math-Net.Ru · dblp
Documents Indexed: 149 Publications since 1966, including 10 Books
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Serials

25 Journal of Mathematical Physics
15 Journal of Physics A: Mathematical and General
8 Dopovidi Akademiï Nauk Ukraïns’koï RSR. Seriya A
7 Czechoslovak Journal of Physics
5 Doklady Akademii Nauk Ukrainskoĭ SSR, Seriya A
5 Letters in Mathematical Physics
5 Ukrainian Mathematical Journal
5 Methods of Functional Analysis and Topology
5 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
4 Ukraïns’kyĭ Matematychnyĭ Zhurnal
4 Journal of Physics A: Mathematical and Theoretical
3 Reports on Mathematical Physics
3 Mathematics and Its Applications. Soviet Series
2 Modern Physics Letters A
2 Journal of Mathematical Analysis and Applications
2 Mathematical Notes
2 Matematicheskie Zametki
2 Teoreticheskaya i Matematicheskaya Fizika
2 Algebras, Groups and Geometries
2 Translations. Series 2. American Mathematical Society
1 Communications in Mathematical Physics
1 Physics Letters. A
1 Russian Mathematical Surveys
1 Theoretical and Mathematical Physics
1 Hadronic Journal
1 International Journal of Mathematics and Mathematical Sciences
1 Soviet Mathematics. Doklady
1 Acta Applicandae Mathematicae
1 CWI Quarterly
1 Dopovidi Akademiï Nauk Ukraïni
1 Integral Transforms and Special Functions
1 Algebras and Representation Theory
1 Dopovidi Natsional’noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky
1 Naukovi Zapysky (Kyïv)
1 Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya
1 Mathematics and its Applications (Dordrecht)
1 Texts and Monographs in Physics

Publications by Year

Citations contained in zbMATH Open

83 Publications have been cited 921 times in 740 Documents Cited by Year
Quantum groups and their representations. Zbl 0891.17010
Klimyk, Anatoli; Schmüdgen, Konrad
236
1997
Representation of Lie groups and special functions. Volume 1: Simplest Lie groups, special functions and integral transforms. Transl. from the Russian by V. A. Groza and A. A. Groza. Zbl 0742.22001
Vilenkin, N. Ya.; Klimyk, A. U.
83
1991
Representation of Lie groups and special functions. Volume 2: Class I representations, special functions, and integral transforms. Zbl 0809.22001
Vilenkin, N. Ya.; Klimyk, A. U.
57
1993
Representation of Lie groups and special functions. Recent advances. Transl. from the Russian by V. A. Groza a. A. A. Groza. Zbl 0826.22001
Vilenkin, N. Ja.; Klimyk, A. U.
45
1994
Representation of Lie groups and special functions. Volume 3: Classical and quantum groups and special functions. Transl. from the Russian by V. A. Groza and A. A. Groza. Zbl 0778.22001
Vilenkin, N. Ya.; Klimyk, A. U.
35
1992
\(P,Q\)-differentiation, \(P,Q\)-integration, and \(P,Q\)-hypergeometric functions related to quantum groups. Zbl 0823.33010
Burban, Ivan M.; Klimyk, Anatoli U.
34
1994
\(q\)-deformed orthogonal and pseudo-orthogonal algebras and their representations. Zbl 0735.17020
Gavrilik, A. M.; Klimyk, A. U.
30
1991
Representations of the quantum algebra \(U_ q(su_{1,1})\). Zbl 0780.17010
Burban, I. M.; Klimyk, A. U.
21
1993
Orbit functions. Zbl 1118.33004
Klimyk, Anatoliy; Patera, Jiri
21
2006
Representation matrix elements and Clebsch-Gordan coefficients of the semisimple Lie groups. Zbl 0416.22017
Klimyk, A. U.; Gavrilik, A. M.
20
1979
On Clebsch-Gordan coefficients and matrix elements of representations of the quantum algebra \(U_ q(su_ 2)\). Zbl 0735.17021
Groza, V. A.; Kachurik, I. I.; Klimyk, A. U.
18
1990
General recurrence relations for Clebsch-Gordan coefficients of the quantum algebra \(U_ q(su_ 2)\). Zbl 0742.33014
Kachurik, I. I.; Klimyk, A. U.
14
1991
Antisymmetric orbit functions. Zbl 1138.33001
Klimyk, Anatoliy; Patera, Jiri
14
2007
Representations of the cyclically symmetric \(q\)-deformed algebra \(\text{so}_q(3)\). Zbl 0959.17015
Havlíček, M.; Klimyk, A. U.; Pošta, S.
14
1999
Classification theorem on irreducible representations of the \(q\)-deformed algebra \(U_q^{\prime}(\text{so}_n)\). Zbl 1127.17016
Iorgov, N. Z.; Klimyk, A. U.
12
2005
Matrix elements and the Clebsch-Gordan coefficients of groups representations. (Matricnye elementy i koefficienty Klebsa-Gordana predstavlenii grupp.). Zbl 0412.22004
Klimyk, A. U.
12
1979
(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms. Zbl 1152.81513
Klimyk, A.; Patera, J.
11
2007
Decomposition of a direct product of irreducible representations of a semisimple Lie algebra into a direct sum of irreducible representations. Zbl 0228.17004
Klimyk, A. U.
11
1966
(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms. Zbl 1139.42001
Klimyk, A. U.; Patera, J.
10
2007
Matrix elements for infinitesimal operators of the groups \(U(p+q)\) and \(U(p,q)\) in a \(U(p)\times U(q)\) basis. I. Zbl 0427.22016
Klimyk, Anatoli U.; Gruber, Bruno
9
1979
On spectral properties of \(q\)-oscillator operators. Zbl 0789.17007
Burban, I. M.; Klimyk, A. U.
9
1993
Representations of Lie groups and special functions. Zbl 0818.22008
Klimyk, A. U.; Vilenkin, N. Ya.
8
1990
The representations of the groups \(U(n,1)\) and \(SO_0(n,1)\). (Predstavlenija grupp \(U(n,1)\) i \(SO_0(n,1)\)). Zbl 0337.22020
Klimyk, A. U.; Gavrilik, A. M.
8
1976
Structure and matrix elements of the degenerate series representations of \(U(p+q)\) and U(p,q) in a U(p)\(\times U(q)\) basis. Zbl 0548.22011
Klimyk, Anatoli U.; Gruber, Bruno
8
1982
\(E\)-orbit functions. Zbl 1139.33001
Klimyk, Anatoliy U.; Patera, Jiri
7
2008
On position and momentum operators in the \(q\)-oscillator algebra. Zbl 0879.47041
Chung, Won-Sang; Klimyk, Anatoli U.
7
1996
Representations of the groups Sp(n,R) and Sp(n) in a U(n) basis. Zbl 0548.22010
Klimyk, Anatoli U.
7
1983
Wigner-Eckart theorem for the quantum group \(U_ q(n)\). Zbl 0761.17013
Klimyk, A. U.
6
1992
Multiplicity free and finite multiplicity indecomposable representations of the algebra su(1,1). Zbl 0425.22023
Gruber, Bruno; Klimyk, A. U.
6
1978
On position and momentum operators in the \(q\)-oscillator. Zbl 1067.81060
Klimyk, A. U.
6
2005
Matrix elements for indecomposable representations of complex su(2). Zbl 0548.17005
Gruber, Bruno; Klimyk, Anatoli U.
6
1984
Big \(q\)-Laguerre and \(q\)-Meixner polynomials and representations of the quantum algebra \(U_q(su_{1,1}\)). Zbl 1058.81040
Atakishiyev, M. N.; Atakishiyev, N. M.; Klimyk, A. U.
6
2003
On \(q\)-orthogonal polynomials, dual to little and big \(q\)-Jacobi polynomials. Zbl 1049.33013
Atakishiyev, N. M.; Klimyk, A. U.
6
2004
On representations of the groups Sp(n,1) and Sp(n). Zbl 0591.22014
Holod, P. I.; Klimyk, A. U.
6
1985
Representations of Lie groups and special functions. Zbl 0727.22007
Vilenkin, N. Ya.; Klimyk, A. U.
5
1990
Properties of linear representations with a highest weight for the semisimple Lie algebras. Zbl 0308.17002
Gruber, B.; Klimyk, A. U.
5
1975
Multiplicities of weights of representations and multiplicities of representations of semisimple Lie algebras. Zbl 0239.17005
Klimyk, A. U.
5
1967
Central elements of the algebras \(U'_q(\text{so}_m)\) and \(U_q(\text{iso}_m)\). Zbl 0977.22005
Havlíček, M.; Klimyk, A. U.; Pošta, S.
5
2000
Nonstandard quantization of the enveloping algebra \(U(\text{so}(n))\) and its applications. Zbl 1248.17013
Klimyk, A. U.
4
2001
Matrix elements for infinitesimal operators of the groups \(U(p+q)\) and \(U(p,q)\) in a \(U(p)\times U(q)\) basis. II. Zbl 0427.22017
Klimyk, A. U.
4
1979
Representations of the groups GL(n,R) and SU(n) in an SO(n) basis. Zbl 0485.22021
Gruber, Bruno; Klimyk, Anatoli U.
4
1981
Representations of the \(q\)-deformed algebras \(U_ q(so_{2,1})\) and \(U_ q(so_{3,1})\). Zbl 0809.17010
Gavrilik, A. M.; Klimyk, A. U.
4
1994
Classical and quantum Heisenberg groups, their representations and applications. Zbl 0857.22007
Klimyk, A. U.; Schempp, W.
4
1996
Representations of the nonstandard (twisted) deformation \(U'_q(\text{so}_n)\) for \(q\) a root of unity. Zbl 1045.22012
Iorgov, N. Z.; Klimyk, A. U.
4
2000
The \(q\)-Laplace operator and \(q\)-harmonic polynomials on the quantum vector space. Zbl 1023.33015
Iorgov, N. Z.; Klimyk, A. U.
4
2001
On Racah coefficients of the quantum algebra \(U_ q(su_ 2)\). Zbl 0708.17018
Kachurik, I. I.; Klimyk, A. U.
4
1990
On \(\text{su}_{q}(1,1)\)-models of quantum oscillator. Zbl 1112.81058
Atakishiyev, M. N.; Atakishiyev, N. M.; Klimyk, A. U.
4
2006
On discrete \(q\)-ultraspherical polynomials and their duals. Zbl 1076.33013
Atakishiyev, N. M.; Klimyk, A. U.
3
2005
Matrix elements of tensor operators. Zbl 0313.22013
Klimyk, A. U.
3
1975
Clebsch-Gordan coefficients for the unitary, orthogonal and symplectic groups and Clebsch-Gordan series for the unitary group. Zbl 0188.29603
Klimyk, A. U.
3
1968
Infinitesimal operators and structure of the most degenerate representations of the groups \(Sp(p+q)\) and Sp(p,q) in an Sp(p)\(\times Sp(q)\) basis. Zbl 0548.22009
Klimyk, A. U.; Gruber, Bruno
3
1984
On classification of irreducible representations of \(q\)-deformed algebra \(U_q'(\operatorname {so}_3)\) related to quantum gravity. Zbl 1040.81043
Klimyk, A. U.
3
2002
Nonstandard \(U_q(\text{so}_3)\) and \(U_q(\text{so}_4)\): Tensor products of representations, oscillator realizations and roots of unity. Zbl 0942.17005
Havlíček, M.; Pelantová, E.; Klimyk, A.
3
1997
The nonstandard deformation \(U_q'(so_n)\) for \(q\) a root of unity. Zbl 0980.17009
Iorgov, N. Z.; Klimyk, A. U.
3
2000
Representations of the \(q\)-deformed algebra \(U_q'(\text{so}_4)\). Zbl 1017.81025
Havlíček, M.; Klimyk, A. U.; Pošta, S.
3
2001
The factorization of a \(q\)-difference equation for continuous \(q\)-Hermite polynomials. Zbl 1120.39015
Atakishiyev, M. N.; Klimyk, A. U.
3
2007
Representations of the quantum algebras \(U_{q}(u_{r,s})\) and \(U_{q}(u_{r+s})\) related to the quantum hyperboloid and sphere. Zbl 0767.17011
Klimyk, A. U.; Pakuliak, S. Z.
2
1992
Representations of the \(q\)-deformed algebra \(U_ q^ \prime ({\mathfrak {so}}_ 4)\). Zbl 0840.17014
Kachurik, I. I.; Klimyk, A. U.
2
1994
Spectra, eigenvectors and overlap functions for representation operators of \(q\)-deformed algebras. Zbl 0846.17013
Klimyk, A. U.; Kachurik, I. I.
2
1996
Finite \(q\)-oscillator. Zbl 1058.81041
Atakishiyev, Natig M.; Klimyk, Anatoliy U.; Wolf, Kurt Bernardo
2
2004
Analysis of the representations of the Lorentz and Euclidean groups of \(n\)-th order. (Analiz predstavlenii n-mernyh grupp Lorenca i Evklida.) Preprint. Zbl 0341.20029
Gavrilik, A. M.; Klimyk, A. U.
2
1975
A discrete quantum model of the harmonic oscillator. Zbl 1138.81016
Atakishiyev, Natig M.; Klimyk, Anatoliy U.; Wolf, Kurt Bernardo
2
2008
Alternating multivariate trigonometric functions and corresponding Fourier transforms. Zbl 1183.33027
Klimyk, A. U.; Patera, J.
2
2008
Representations of the group SU(1,1) and the Krawtchouk-Meixner functions. Zbl 0645.33020
Vilenkin, N. Ya.; Klimyk, A. U.
2
1988
Alternating group and multivariate exponential functions. Zbl 1184.42007
Klimyk, Anatoliy; Patera, Jiří
1
2009
Matrix elements and Casimir operators of the discrete series representations of the group U(p,q). Zbl 0418.22018
Klimyk, A. U.
1
1979
Representation for matrix elements of compact Lie groups. Zbl 0449.22020
Klimyk, A. U.
1
1980
Matrix elements of representations of the group ISO(n). Zbl 0489.22014
Kachurik, I. I.; Klimyk, A. U.
1
1981
Standard isorepresentations of isotopic/\(Q\)-operator-deformations of Lie algebras. Zbl 0803.17002
Klimyk, Anatoli U.; Santilli, Ruggero M.
1
1993
Operator spectra for quantum algebras and \(q\)-orthogonal polynomials. Zbl 0833.17012
Kachurik, I. I.; Klimyk, A. U.
1
1994
Symmetries of Clebsch-Gordan coefficients of the quantum group \(U_ q(n)\). Zbl 0832.17014
Klimyk, A. U.
1
1995
Representations of the quantum algebra \(U_{q,s}({\mathfrak s} {\mathfrak u}_{1,1})\). Zbl 0832.17015
Klimyk, A. U.
1
1993
\(q\)-deformed Euclidean algebras and their representations. Zbl 0856.17011
Groza, V. A.; Kachurik, I. I.; Klimyk, A. U.
1
1995
On the tensor product of representations of semisimple Lie groups. Zbl 0354.22017
Klimyk, A. U.
1
1977
On characters of irreducible representations with integer highest weight of a semisimple Lie algebra. Zbl 0184.06003
Klimyk, A. U.
1
1968
Wigner-Eckart theorem and infinitesimal operators of group representations. Zbl 0578.22025
Klimyk, A. U.
1
1983
Decomposition of highest-weight representations of a semisimple Lie algebra into representations of regular subalgebras. Zbl 0228.17005
Klimyk, A. U.
1
1970
Infinitesimal operators of group representations in noncanonical bases. Zbl 0681.22019
Klimyk, A. U.; Kachurik, I. I.
1
1988
The representation of \(q\)-deformed algebras \(U_ q(so_{3,1})\), \(U_ q(so_ 4)\) and \(q\)-orthogonal polynomials. Zbl 0886.17010
Kachurik, I. I.; Klimyk, A. U.
1
1993
The embedding \(\text{U}_q^\prime(\text{so}_3)\subset\text{U}_q(\text{sl}_3)\). Zbl 1022.17010
Kachurik, I. I.; Klimyk, A. U.
1
2001
Nonclassical type representations of the \(q\)-deformed algebra \(U_q'(\text{so}_n)\). Zbl 0979.17006
Iorgov, N. Z.; Klimyk, A. U.
1
2000
Jacobi matrix pair and dual alternative \(q\)-Charlier polynomials. Zbl 1097.33014
Atakishiyev, N. M.; Klimyk, A. U.
1
2005
Spectra of observables in the \(q\)-oscillator and \(q\)-analogue of the Fourier transform. Zbl 1098.81035
Klimyk, Anatoliy U.
1
2005
Alternating group and multivariate exponential functions. Zbl 1184.42007
Klimyk, Anatoliy; Patera, Jiří
1
2009
\(E\)-orbit functions. Zbl 1139.33001
Klimyk, Anatoliy U.; Patera, Jiri
7
2008
A discrete quantum model of the harmonic oscillator. Zbl 1138.81016
Atakishiyev, Natig M.; Klimyk, Anatoliy U.; Wolf, Kurt Bernardo
2
2008
Alternating multivariate trigonometric functions and corresponding Fourier transforms. Zbl 1183.33027
Klimyk, A. U.; Patera, J.
2
2008
Antisymmetric orbit functions. Zbl 1138.33001
Klimyk, Anatoliy; Patera, Jiri
14
2007
(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms. Zbl 1152.81513
Klimyk, A.; Patera, J.
11
2007
(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms. Zbl 1139.42001
Klimyk, A. U.; Patera, J.
10
2007
The factorization of a \(q\)-difference equation for continuous \(q\)-Hermite polynomials. Zbl 1120.39015
Atakishiyev, M. N.; Klimyk, A. U.
3
2007
Orbit functions. Zbl 1118.33004
Klimyk, Anatoliy; Patera, Jiri
21
2006
On \(\text{su}_{q}(1,1)\)-models of quantum oscillator. Zbl 1112.81058
Atakishiyev, M. N.; Atakishiyev, N. M.; Klimyk, A. U.
4
2006
Classification theorem on irreducible representations of the \(q\)-deformed algebra \(U_q^{\prime}(\text{so}_n)\). Zbl 1127.17016
Iorgov, N. Z.; Klimyk, A. U.
12
2005
On position and momentum operators in the \(q\)-oscillator. Zbl 1067.81060
Klimyk, A. U.
6
2005
On discrete \(q\)-ultraspherical polynomials and their duals. Zbl 1076.33013
Atakishiyev, N. M.; Klimyk, A. U.
3
2005
Jacobi matrix pair and dual alternative \(q\)-Charlier polynomials. Zbl 1097.33014
Atakishiyev, N. M.; Klimyk, A. U.
1
2005
Spectra of observables in the \(q\)-oscillator and \(q\)-analogue of the Fourier transform. Zbl 1098.81035
Klimyk, Anatoliy U.
1
2005
On \(q\)-orthogonal polynomials, dual to little and big \(q\)-Jacobi polynomials. Zbl 1049.33013
Atakishiyev, N. M.; Klimyk, A. U.
6
2004
Finite \(q\)-oscillator. Zbl 1058.81041
Atakishiyev, Natig M.; Klimyk, Anatoliy U.; Wolf, Kurt Bernardo
2
2004
Big \(q\)-Laguerre and \(q\)-Meixner polynomials and representations of the quantum algebra \(U_q(su_{1,1}\)). Zbl 1058.81040
Atakishiyev, M. N.; Atakishiyev, N. M.; Klimyk, A. U.
6
2003
On classification of irreducible representations of \(q\)-deformed algebra \(U_q'(\operatorname {so}_3)\) related to quantum gravity. Zbl 1040.81043
Klimyk, A. U.
3
2002
Nonstandard quantization of the enveloping algebra \(U(\text{so}(n))\) and its applications. Zbl 1248.17013
Klimyk, A. U.
4
2001
The \(q\)-Laplace operator and \(q\)-harmonic polynomials on the quantum vector space. Zbl 1023.33015
Iorgov, N. Z.; Klimyk, A. U.
4
2001
Representations of the \(q\)-deformed algebra \(U_q'(\text{so}_4)\). Zbl 1017.81025
Havlíček, M.; Klimyk, A. U.; Pošta, S.
3
2001
The embedding \(\text{U}_q^\prime(\text{so}_3)\subset\text{U}_q(\text{sl}_3)\). Zbl 1022.17010
Kachurik, I. I.; Klimyk, A. U.
1
2001
Central elements of the algebras \(U'_q(\text{so}_m)\) and \(U_q(\text{iso}_m)\). Zbl 0977.22005
Havlíček, M.; Klimyk, A. U.; Pošta, S.
5
2000
Representations of the nonstandard (twisted) deformation \(U'_q(\text{so}_n)\) for \(q\) a root of unity. Zbl 1045.22012
Iorgov, N. Z.; Klimyk, A. U.
4
2000
The nonstandard deformation \(U_q'(so_n)\) for \(q\) a root of unity. Zbl 0980.17009
Iorgov, N. Z.; Klimyk, A. U.
3
2000
Nonclassical type representations of the \(q\)-deformed algebra \(U_q'(\text{so}_n)\). Zbl 0979.17006
Iorgov, N. Z.; Klimyk, A. U.
1
2000
Representations of the cyclically symmetric \(q\)-deformed algebra \(\text{so}_q(3)\). Zbl 0959.17015
Havlíček, M.; Klimyk, A. U.; Pošta, S.
14
1999
Quantum groups and their representations. Zbl 0891.17010
Klimyk, Anatoli; Schmüdgen, Konrad
236
1997
Nonstandard \(U_q(\text{so}_3)\) and \(U_q(\text{so}_4)\): Tensor products of representations, oscillator realizations and roots of unity. Zbl 0942.17005
Havlíček, M.; Pelantová, E.; Klimyk, A.
3
1997
On position and momentum operators in the \(q\)-oscillator algebra. Zbl 0879.47041
Chung, Won-Sang; Klimyk, Anatoli U.
7
1996
Classical and quantum Heisenberg groups, their representations and applications. Zbl 0857.22007
Klimyk, A. U.; Schempp, W.
4
1996
Spectra, eigenvectors and overlap functions for representation operators of \(q\)-deformed algebras. Zbl 0846.17013
Klimyk, A. U.; Kachurik, I. I.
2
1996
Symmetries of Clebsch-Gordan coefficients of the quantum group \(U_ q(n)\). Zbl 0832.17014
Klimyk, A. U.
1
1995
\(q\)-deformed Euclidean algebras and their representations. Zbl 0856.17011
Groza, V. A.; Kachurik, I. I.; Klimyk, A. U.
1
1995
Representation of Lie groups and special functions. Recent advances. Transl. from the Russian by V. A. Groza a. A. A. Groza. Zbl 0826.22001
Vilenkin, N. Ja.; Klimyk, A. U.
45
1994
\(P,Q\)-differentiation, \(P,Q\)-integration, and \(P,Q\)-hypergeometric functions related to quantum groups. Zbl 0823.33010
Burban, Ivan M.; Klimyk, Anatoli U.
34
1994
Representations of the \(q\)-deformed algebras \(U_ q(so_{2,1})\) and \(U_ q(so_{3,1})\). Zbl 0809.17010
Gavrilik, A. M.; Klimyk, A. U.
4
1994
Representations of the \(q\)-deformed algebra \(U_ q^ \prime ({\mathfrak {so}}_ 4)\). Zbl 0840.17014
Kachurik, I. I.; Klimyk, A. U.
2
1994
Operator spectra for quantum algebras and \(q\)-orthogonal polynomials. Zbl 0833.17012
Kachurik, I. I.; Klimyk, A. U.
1
1994
Representation of Lie groups and special functions. Volume 2: Class I representations, special functions, and integral transforms. Zbl 0809.22001
Vilenkin, N. Ya.; Klimyk, A. U.
57
1993
Representations of the quantum algebra \(U_ q(su_{1,1})\). Zbl 0780.17010
Burban, I. M.; Klimyk, A. U.
21
1993
On spectral properties of \(q\)-oscillator operators. Zbl 0789.17007
Burban, I. M.; Klimyk, A. U.
9
1993
Standard isorepresentations of isotopic/\(Q\)-operator-deformations of Lie algebras. Zbl 0803.17002
Klimyk, Anatoli U.; Santilli, Ruggero M.
1
1993
Representations of the quantum algebra \(U_{q,s}({\mathfrak s} {\mathfrak u}_{1,1})\). Zbl 0832.17015
Klimyk, A. U.
1
1993
The representation of \(q\)-deformed algebras \(U_ q(so_{3,1})\), \(U_ q(so_ 4)\) and \(q\)-orthogonal polynomials. Zbl 0886.17010
Kachurik, I. I.; Klimyk, A. U.
1
1993
Representation of Lie groups and special functions. Volume 3: Classical and quantum groups and special functions. Transl. from the Russian by V. A. Groza and A. A. Groza. Zbl 0778.22001
Vilenkin, N. Ya.; Klimyk, A. U.
35
1992
Wigner-Eckart theorem for the quantum group \(U_ q(n)\). Zbl 0761.17013
Klimyk, A. U.
6
1992
Representations of the quantum algebras \(U_{q}(u_{r,s})\) and \(U_{q}(u_{r+s})\) related to the quantum hyperboloid and sphere. Zbl 0767.17011
Klimyk, A. U.; Pakuliak, S. Z.
2
1992
Representation of Lie groups and special functions. Volume 1: Simplest Lie groups, special functions and integral transforms. Transl. from the Russian by V. A. Groza and A. A. Groza. Zbl 0742.22001
Vilenkin, N. Ya.; Klimyk, A. U.
83
1991
\(q\)-deformed orthogonal and pseudo-orthogonal algebras and their representations. Zbl 0735.17020
Gavrilik, A. M.; Klimyk, A. U.
30
1991
General recurrence relations for Clebsch-Gordan coefficients of the quantum algebra \(U_ q(su_ 2)\). Zbl 0742.33014
Kachurik, I. I.; Klimyk, A. U.
14
1991
On Clebsch-Gordan coefficients and matrix elements of representations of the quantum algebra \(U_ q(su_ 2)\). Zbl 0735.17021
Groza, V. A.; Kachurik, I. I.; Klimyk, A. U.
18
1990
Representations of Lie groups and special functions. Zbl 0818.22008
Klimyk, A. U.; Vilenkin, N. Ya.
8
1990
Representations of Lie groups and special functions. Zbl 0727.22007
Vilenkin, N. Ya.; Klimyk, A. U.
5
1990
On Racah coefficients of the quantum algebra \(U_ q(su_ 2)\). Zbl 0708.17018
Kachurik, I. I.; Klimyk, A. U.
4
1990
Representations of the group SU(1,1) and the Krawtchouk-Meixner functions. Zbl 0645.33020
Vilenkin, N. Ya.; Klimyk, A. U.
2
1988
Infinitesimal operators of group representations in noncanonical bases. Zbl 0681.22019
Klimyk, A. U.; Kachurik, I. I.
1
1988
On representations of the groups Sp(n,1) and Sp(n). Zbl 0591.22014
Holod, P. I.; Klimyk, A. U.
6
1985
Matrix elements for indecomposable representations of complex su(2). Zbl 0548.17005
Gruber, Bruno; Klimyk, Anatoli U.
6
1984
Infinitesimal operators and structure of the most degenerate representations of the groups \(Sp(p+q)\) and Sp(p,q) in an Sp(p)\(\times Sp(q)\) basis. Zbl 0548.22009
Klimyk, A. U.; Gruber, Bruno
3
1984
Representations of the groups Sp(n,R) and Sp(n) in a U(n) basis. Zbl 0548.22010
Klimyk, Anatoli U.
7
1983
Wigner-Eckart theorem and infinitesimal operators of group representations. Zbl 0578.22025
Klimyk, A. U.
1
1983
Structure and matrix elements of the degenerate series representations of \(U(p+q)\) and U(p,q) in a U(p)\(\times U(q)\) basis. Zbl 0548.22011
Klimyk, Anatoli U.; Gruber, Bruno
8
1982
Representations of the groups GL(n,R) and SU(n) in an SO(n) basis. Zbl 0485.22021
Gruber, Bruno; Klimyk, Anatoli U.
4
1981
Matrix elements of representations of the group ISO(n). Zbl 0489.22014
Kachurik, I. I.; Klimyk, A. U.
1
1981
Representation for matrix elements of compact Lie groups. Zbl 0449.22020
Klimyk, A. U.
1
1980
Representation matrix elements and Clebsch-Gordan coefficients of the semisimple Lie groups. Zbl 0416.22017
Klimyk, A. U.; Gavrilik, A. M.
20
1979
Matrix elements and the Clebsch-Gordan coefficients of groups representations. (Matricnye elementy i koefficienty Klebsa-Gordana predstavlenii grupp.). Zbl 0412.22004
Klimyk, A. U.
12
1979
Matrix elements for infinitesimal operators of the groups \(U(p+q)\) and \(U(p,q)\) in a \(U(p)\times U(q)\) basis. I. Zbl 0427.22016
Klimyk, Anatoli U.; Gruber, Bruno
9
1979
Matrix elements for infinitesimal operators of the groups \(U(p+q)\) and \(U(p,q)\) in a \(U(p)\times U(q)\) basis. II. Zbl 0427.22017
Klimyk, A. U.
4
1979
Matrix elements and Casimir operators of the discrete series representations of the group U(p,q). Zbl 0418.22018
Klimyk, A. U.
1
1979
Multiplicity free and finite multiplicity indecomposable representations of the algebra su(1,1). Zbl 0425.22023
Gruber, Bruno; Klimyk, A. U.
6
1978
On the tensor product of representations of semisimple Lie groups. Zbl 0354.22017
Klimyk, A. U.
1
1977
The representations of the groups \(U(n,1)\) and \(SO_0(n,1)\). (Predstavlenija grupp \(U(n,1)\) i \(SO_0(n,1)\)). Zbl 0337.22020
Klimyk, A. U.; Gavrilik, A. M.
8
1976
Properties of linear representations with a highest weight for the semisimple Lie algebras. Zbl 0308.17002
Gruber, B.; Klimyk, A. U.
5
1975
Matrix elements of tensor operators. Zbl 0313.22013
Klimyk, A. U.
3
1975
Analysis of the representations of the Lorentz and Euclidean groups of \(n\)-th order. (Analiz predstavlenii n-mernyh grupp Lorenca i Evklida.) Preprint. Zbl 0341.20029
Gavrilik, A. M.; Klimyk, A. U.
2
1975
Decomposition of highest-weight representations of a semisimple Lie algebra into representations of regular subalgebras. Zbl 0228.17005
Klimyk, A. U.
1
1970
Clebsch-Gordan coefficients for the unitary, orthogonal and symplectic groups and Clebsch-Gordan series for the unitary group. Zbl 0188.29603
Klimyk, A. U.
3
1968
On characters of irreducible representations with integer highest weight of a semisimple Lie algebra. Zbl 0184.06003
Klimyk, A. U.
1
1968
Multiplicities of weights of representations and multiplicities of representations of semisimple Lie algebras. Zbl 0239.17005
Klimyk, A. U.
5
1967
Decomposition of a direct product of irreducible representations of a semisimple Lie algebra into a direct sum of irreducible representations. Zbl 0228.17004
Klimyk, A. U.
11
1966
all top 5

Cited by 859 Authors

38 Klimyk, Anatoliy Ul’yanovich
15 Vinet, Luc
13 Marinucci, Domenico
12 Atakishiev, Natig M.
12 Patera, Jiří
11 Rubin, Boris
10 Fakhri, Hossein
9 Hrivnák, Jiří
9 Landi, Giovanni
8 Genest, Vincent X.
8 Gruber, Bruno J.
8 Kolb, Stefan
7 Chirvăsitu, Alexandru
7 Gavrilik, Alexandre M.
7 Heckenberger, István
7 Kachurik, Ivan I.
7 Koelink, Erik
7 Krähmer, Ulrich
7 Van der Jeugt, Joris
6 Acar, Tuncer
6 Hu, Naihong
6 Matassa, Marco
6 Sahai, Vivek
6 Terwilliger, Paul M.
6 van Diejen, Jan Felipe
5 Bichon, Julien
5 Damaskinskij, E. V.
5 De Commer, Kenny
5 Emsiz, Erdal
5 Ó Buachalla, Réamonn
5 Saurabh, Bipul
5 Schmüdgen, Konrad
5 Szajewska, Marzena
5 Yadav, Sarasvati
5 Zhedanov, Alexei S.
4 Ališauskas, Sigitas
4 Aral, Ali
4 Area, Iván
4 Baseilhac, Pascal
4 Crampé, Nicolas
4 D’Andrea, Francesco
4 Fioresi, Rita
4 Geller, Daryl
4 Hartwig, Jonas T.
4 Havlíček, Miloslav
4 Hounkonnou, Mahouton Norbert
4 Huang, Hau-wen
4 Mohiuddine, Syed Abdul
4 Molev, Alexander I.
4 Motlochová, Lenka
4 Pošta, Severin
4 Ragoucy, Eric
4 Ruzhansky, Michael V.
4 Sayyah-Fard, M.
4 Scarabotti, Fabio
4 Sokolov, M. A.
3 Atakishiyeva, Mesuma K.
3 Chakraborty, Partha Sarathi
3 Chirikjian, Gregory S.
3 Ciccoli, Nicola
3 Dabrowski, Ludwik
3 Finkelstein, Robert J.
3 Gaboriaud, Julien
3 Gade, R. M.
3 Geyer, Bodo
3 Hadfield, Tom
3 Kaad, Jens
3 Kharchenko, Vladislav K.
3 Knapp, Anthony William
3 Koornwinder, Tom H.
3 Kravchuk, Petr
3 Kulish, Petr Petrovich
3 Kyed, David
3 Lazar, Markus
3 Lievens, Stijn
3 Lowe, David A.
3 Man’ko, Vladimir Ivanovich
3 Masjed-Jamei, Mohammad
3 Morozov, Alexei Yurievich
3 Morozov, Andreĭ Alekseevich
3 Neshveyev, Sergey V.
3 Niedermaier, Max R.
3 Nomura, Kazumasa
3 Nouraddini, Mojtaba
3 Orlov, Aleksandr Yu.
3 Pacharoni, Inés
3 Pagani, Chiara
3 Pan, Feng
3 Peccati, Giovanni
3 Quesne, Christiane
3 Razumov, Alexander V.
3 Rozenblyum, Alexander V.
3 Schneider, Hans-Jürgen
3 Soleyman, F.
3 Somberg, Petr
3 Stoilova, Nedjalka I.
3 Stokman, Jasper V.
3 Tirao, Juan
3 Wagner, Elmar
3 Wenzl, Hans
...and 759 more Authors
all top 5

Cited in 179 Serials

109 Journal of Mathematical Physics
43 Journal of Algebra
34 Communications in Mathematical Physics
32 Nuclear Physics. B
24 Letters in Mathematical Physics
24 Theoretical and Mathematical Physics
19 Journal of Geometry and Physics
18 Journal of Functional Analysis
16 Journal of Mathematical Analysis and Applications
16 Advances in Mathematics
12 Journal of Pure and Applied Algebra
12 Journal of High Energy Physics
11 Linear Algebra and its Applications
10 Reports on Mathematical Physics
10 Journal of Computational and Applied Mathematics
10 Transactions of the American Mathematical Society
9 The Journal of Fourier Analysis and Applications
9 The Ramanujan Journal
9 Algebras and Representation Theory
8 International Journal of Theoretical Physics
7 Journal of Mathematical Sciences (New York)
7 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
6 Communications in Algebra
6 Physics Letters. A
6 Advances in Applied Clifford Algebras
6 International Journal of Geometric Methods in Modern Physics
5 Israel Journal of Mathematics
5 Ukrainian Mathematical Journal
5 Reviews in Mathematical Physics
5 Journal of Approximation Theory
5 Representation Theory
5 Annales Henri Poincaré
4 Modern Physics Letters A
4 Physics Letters. B
4 Annales de l’Institut Fourier
4 Duke Mathematical Journal
4 Proceedings of the American Mathematical Society
4 Acta Applicandae Mathematicae
4 Annals of Physics
4 Applied and Computational Harmonic Analysis
4 Journal of Nonlinear Mathematical Physics
4 Journal of Noncommutative Geometry
3 Compositio Mathematica
3 Publications of the Research Institute for Mathematical Sciences, Kyoto University
3 Advances in Applied Mathematics
3 Expositiones Mathematicae
3 Indagationes Mathematicae. New Series
3 Selecta Mathematica. New Series
3 Annals of Mathematics. Second Series
3 Journal of Algebra and its Applications
3 Journal of \(K\)-Theory
3 Journal of Function Spaces
2 International Journal of Modern Physics A
2 Mathematical Notes
2 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique
2 Applied Mathematics and Computation
2 International Journal of Mathematics and Mathematical Sciences
2 Integral Equations and Operator Theory
2 Journal of Combinatorial Theory. Series A
2 Journal of Multivariate Analysis
2 Journal of Number Theory
2 Mathematische Annalen
2 Mathematische Nachrichten
2 Statistics & Probability Letters
2 Chinese Annals of Mathematics. Series B
2 Probability Theory and Related Fields
2 Applied Mathematics Letters
2 Forum Mathematicum
2 International Journal of Mathematics
2 The Journal of Geometric Analysis
2 Godishnik na Sofiĭskiya Universitet “Sv. Kliment Okhridski”. Fakultet po Matematika i Informatika
2 Integral Transforms and Special Functions
2 Journal of Inequalities and Applications
2 Iranian Journal of Science and Technology. Transaction A: Science
2 Foundations of Physics
2 Complex Analysis and Operator Theory
2 Journal of Physics A: Mathematical and Theoretical
2 Banach Journal of Mathematical Analysis
2 Advances in Mathematical Physics
2 Science China. Mathematics
1 Applicable Analysis
1 Computers & Mathematics with Applications
1 Computer Physics Communications
1 Inverse Problems
1 Journal d’Analyse Mathématique
1 Journal of Statistical Physics
1 Linear and Multilinear Algebra
1 Mathematical Methods in the Applied Sciences
1 Physica A
1 Russian Mathematical Surveys
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Beiträge zur Algebra und Geometrie
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 The Annals of Statistics
1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
1 Bulletin of the London Mathematical Society
1 Functional Analysis and its Applications
1 Geometriae Dedicata
1 Inventiones Mathematicae
1 Journal of Differential Equations
...and 79 more Serials
all top 5

Cited in 55 Fields

295 Quantum theory (81-XX)
255 Nonassociative rings and algebras (17-XX)
165 Special functions (33-XX)
127 Topological groups, Lie groups (22-XX)
117 Associative rings and algebras (16-XX)
71 Group theory and generalizations (20-XX)
70 Functional analysis (46-XX)
65 Global analysis, analysis on manifolds (58-XX)
32 Combinatorics (05-XX)
32 Harmonic analysis on Euclidean spaces (42-XX)
31 Abstract harmonic analysis (43-XX)
29 Probability theory and stochastic processes (60-XX)
29 Statistical mechanics, structure of matter (82-XX)
27 Operator theory (47-XX)
26 Relativity and gravitational theory (83-XX)
24 Partial differential equations (35-XX)
23 Algebraic geometry (14-XX)
22 Differential geometry (53-XX)
21 Linear and multilinear algebra; matrix theory (15-XX)
21 Integral transforms, operational calculus (44-XX)
18 Numerical analysis (65-XX)
17 Category theory; homological algebra (18-XX)
17 Approximations and expansions (41-XX)
15 Difference and functional equations (39-XX)
15 Manifolds and cell complexes (57-XX)
14 Number theory (11-XX)
14 Dynamical systems and ergodic theory (37-XX)
10 Statistics (62-XX)
9 \(K\)-theory (19-XX)
9 Functions of a complex variable (30-XX)
8 Several complex variables and analytic spaces (32-XX)
8 Ordinary differential equations (34-XX)
7 Computer science (68-XX)
6 Convex and discrete geometry (52-XX)
6 Mechanics of particles and systems (70-XX)
5 Geometry (51-XX)
5 Biology and other natural sciences (92-XX)
5 Information and communication theory, circuits (94-XX)
4 Algebraic topology (55-XX)
4 Astronomy and astrophysics (85-XX)
4 Operations research, mathematical programming (90-XX)
3 Mathematical logic and foundations (03-XX)
2 Order, lattices, ordered algebraic structures (06-XX)
2 Commutative algebra (13-XX)
2 Real functions (26-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Measure and integration (28-XX)
1 Integral equations (45-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 Mechanics of deformable solids (74-XX)
1 Fluid mechanics (76-XX)
1 Optics, electromagnetic theory (78-XX)
1 Geophysics (86-XX)
1 Systems theory; control (93-XX)

Citations by Year