## Terwilliger, Paul M.

Compute Distance To:
 Author ID: terwilliger.paul-m Published as: Terwilliger, Paul; Terwilliger, Paul M.; Terwilliger, P.
 Documents Indexed: 135 Publications since 1982 Co-Authors: 25 Co-Authors with 73 Joint Publications 551 Co-Co-Authors
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### Co-Authors

 62 single-authored 24 Nomura, Kazumasa 20 Ito, Tatsuro 4 Jurišić, Aleksandar 4 Žitnik, Arjana 3 Benkart, Georgia M. 3 MacLean, Mark S. 3 Weng, Chih-Wen 2 Dickie, Garth A. 2 Koolen, Jack H. 2 Miklavič, Štefko 1 Bockting-Conrad, Sarah 1 Caughman, John S. IV 1 Cioabă, Sebastian M. 1 Deza, Michel Marie 1 Ding, Kequan 1 Go, Junie T. 1 Hartwig, Brian 1 Iliev, Plamen 1 Lang, Michael S. 1 Pascasio, Arlene A. 1 Post, Sarah 1 Rosengren, Hjalmar 1 Tanabe, Kenichiro 1 Vidunas, Raimundas 1 Worawannotai, Chalermpong
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### Serials

 34 Linear Algebra and its Applications 10 Journal of Algebra 10 European Journal of Combinatorics 8 Discrete Mathematics 8 Journal of Algebraic Combinatorics 7 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 6 Journal of Combinatorial Theory. Series A 6 Journal of Combinatorial Theory. Series B 5 Journal of Algebra and its Applications 4 Nuclear Physics. B 4 Graphs and Combinatorics 3 ELA. The Electronic Journal of Linear Algebra 2 Communications in Algebra 2 Journal of Computational and Applied Mathematics 2 Journal of Pure and Applied Algebra 2 Ars Mathematica Contemporanea 1 Communications in Mathematical Physics 1 Journal of Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Journal of Combinatorics, Information & System Sciences 1 Mathematische Zeitschrift 1 Michigan Mathematical Journal 1 Proceedings of the American Mathematical Society 1 Transactions of the American Mathematical Society 1 Combinatorica 1 Designs, Codes and Cryptography 1 Algebras, Groups and Geometries 1 Kyushu Journal of Mathematics 1 The Ramanujan Journal 1 RIMS Kokyuroku 1 Special Matrices 1 Algebraic Combinatorics
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### Fields

 90 Combinatorics (05-XX) 45 Nonassociative rings and algebras (17-XX) 39 Special functions (33-XX) 38 Linear and multilinear algebra; matrix theory (15-XX) 10 Associative rings and algebras (16-XX) 10 Quantum theory (81-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 2 Geometry (51-XX) 2 Algebraic topology (55-XX) 1 $$K$$-theory (19-XX) 1 Group theory and generalizations (20-XX) 1 Ordinary differential equations (34-XX) 1 Functional analysis (46-XX)

### Citations contained in zbMATH Open

128 Publications have been cited 2,865 times in 622 Documents Cited by Year
The subconstituent algebra of an association scheme. I. Zbl 0785.05089
Terwilliger, Paul
1992
Two linear transformations each tridiagonal with respect to an eigenbasis of the other. Zbl 0980.05054
Terwilliger, Paul
2001
The subconstituent algebra of an association scheme. III. Zbl 0785.05091
Terwilliger, Paul
1993
Some algebra related to $$P$$- and $$Q$$-polynomial association schemes. Zbl 0995.05148
Ito, Tatsuro; Tanabe, Kenichiro; Terwilliger, Paul
2001
Two relations that generalize the $$q$$-Serre relations and the Dolan-Grady relations. Zbl 1061.16033
Terwilliger, Paul
2001
Leonard pairs and the Askey-Wilson relations. Zbl 1062.33018
Terwilliger, Paul; Vidunas, Raimundas
2004
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array. Zbl 1063.05138
Terwilliger, Paul
2005
The subconstituent algebra of an association scheme. II. Zbl 0785.05090
Terwilliger, Paul
1993
Leonard pairs and the $$q$$-Racah polynomials. Zbl 1075.05090
Terwilliger, Paul
2004
An algebraic approach to the Askey scheme of orthogonal polynomials. Zbl 1102.33011
Terwilliger, Paul
2006
Tridiagonal pairs and the quantum affine algebra $$U_q(\widehat{\text{sl}}_2)$$. Zbl 1128.16028
Ito, Tatsuro; Terwilliger, Paul
2007
Leonard pairs from 24 points of view. Zbl 1040.05030
Terwilliger, Paul
2002
Introduction to Leonard pairs. Zbl 1035.05103
Terwilliger, Paul
2003
The quantum algebra $$U_q(\mathfrak{sl}_2)$$ and its equitable presentation. Zbl 1090.17004
Ito, Tatsuro; Terwilliger, Paul; Weng, Chih-Wen
2006
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form. Zbl 1079.15005
Terwilliger, Paul
2005
The shape of a tridiagonal pair. Zbl 1037.17013
Ito, Tatsuro; Terwilliger, Paul
2004
The tetrahedron algebra, the Onsager algebra, and the $$\mathfrak{sl}_2$$ loop algebra. Zbl 1163.17026
Hartwig, Brian; Terwilliger, Paul
2007
The $$q$$-tetrahedron algebra and its finite dimensional irreducible modules. Zbl 1133.17011
Ito, Tatsuro; Terwilliger, Paul
2007
The universal Askey-Wilson algebra. Zbl 1244.33015
Terwilliger, Paul
2011
Tight distance-regular graphs. Zbl 0959.05121
Jurišić, Aleksandar; Koolen, Jack; Terwilliger, Paul
2000
Two non-nilpotent linear transformations that satisfy the cubic $$q$$-Serre relations. Zbl 1179.17017
Ito, Tatsuro; Terwilliger, Paul
2007
The augmented tridiagonal algebra. Zbl 1236.17022
Ito, Tatsuro; Terwilliger, Paul
2010
Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair. Zbl 1119.05111
Nomura, Kazumasa; Terwilliger, Paul
2007
A new inequality for distance-regular graphs. Zbl 0814.05074
Terwilliger, Paul
1995
Two linear transformations each tridiagonal with respect to an eigenbasis of the other: comments on the split decomposition. Zbl 1069.15005
Terwilliger, Paul
2005
The equitable presentation for the quantum group associated with a symmetrizable Kac-Moody algebra. Zbl 1106.17021
Terwilliger, Paul
2006
Finite-dimensional irreducible modules for the three-point $$\mathfrak{sl}_2$$ loop algebra. Zbl 1207.17030
Ito, Tatsuro; Terwilliger, Paul
2008
Tight distance-regular graphs and the subconstituent algebra. Zbl 1014.05070
Go, Junie T.; Terwilliger, Paul
2002
Tridiagonal pairs of $$q$$-Racah type. Zbl 1177.33021
Ito, Tatsuro; Terwilliger, Paul
2009
The universal Askey-Wilson algebra and the equitable presentation of $$U_{q}(sl_{2})$$. Zbl 1244.33016
Terwilliger, Paul
2011
The universal Askey-Wilson algebra and DAHA of type $$(C_{1}^{\vee },C_{1})$$. Zbl 1293.33022
Terwilliger, Paul
2013
A characterization of $$P$$- and $$Q$$-polynomial association schemes. Zbl 0663.05016
Terwilliger, Paul
1987
Affine transformations of a Leonard pair. Zbl 1143.05337
Nomura, Kazumasa; Terwilliger, Paul
2007
Distance-regular graphs and the $$q$$-tetrahedron algebra. Zbl 1193.17008
Ito, Tatsuro; Terwilliger, Paul
2009
A note on thin $$P$$-polynomial and dual-thin $$Q$$-polynomial symmetric association schemes. Zbl 0898.05084
Dickie, Garth A.; Terwilliger, Paul M.
1998
The universal central extension of the three-point $$\mathfrak{sl}_2$$ loop algebra. Zbl 1153.17008
Benkart, Georgia; Terwilliger, Paul
2007
A new feasibility condition for distance-regular graphs. Zbl 0606.05045
Terwilliger, Paul
1986
Balanced Leonard pairs. Zbl 1119.05110
Nomura, Kazumasa; Terwilliger, Paul
2007
The incidence algebra of a uniform poset. Zbl 0737.05032
Terwilliger, Paul
1990
$$p$$-inverting pairs of linear transformations and the $$q$$-tetrahedron algebra. Zbl 1146.17009
Ito, Tatsuro; Terwilliger, Paul
2007
Tridiagonal pairs of Krawtchouk type. Zbl 1132.15010
Ito, Tatsuro; Terwilliger, Paul
2007
Irreducible modules for the quantum affine algebra $$U_{q}(\mathfrak {\widehat{sl}_2})$$ and its Borel subalgebra. Zbl 1106.17014
Benkart, Georgia; Terwilliger, Paul
2004
Distance-regular graphs and (s,c,a,k)-graphs. Zbl 0511.05052
Terwilliger, Paul
1983
Some trace formulae involving the split sequences of a Leonard pair. Zbl 1085.05070
Nomura, Kazumasa; Terwilliger, Paul
2006
The structure of a tridiagonal pair. Zbl 1144.05331
Nomura, Kazumasa; Terwilliger, Paul
2008
An introduction to Leonard pairs and Leonard systems. Zbl 0957.15500
Terwilliger, Paul
1999
A classification of sharp tridiagonal pairs. Zbl 1225.15015
Ito, Tatsuro; Nomura, Kazumasa; Terwilliger, Paul
2011
Kite-free distance-regular graphs. Zbl 0829.05059
Terwilliger, Paul
1995
Sharp tridiagonal pairs. Zbl 1193.05164
Nomura, Kazumasa; Terwilliger, Paul
2008
Matrix units associated with the split basis of a Leonard pair. Zbl 1107.05103
Nomura, Kazumasa; Terwilliger, Paul
2006
The equitable basis for $${\mathfrak{sl}_2}$$. Zbl 1277.17013
Benkart, Georgia; Terwilliger, Paul
2011
Distance-regular graphs with girth 3 or 4: I. Zbl 0588.05039
Terwilliger, Paul
1985
Root systems and the Johnson and Hamming graphs. Zbl 0614.05048
Terwilliger, Paul
1987
The Terwilliger algebra of an almost-bipartite $$P$$- and $$Q$$-polynomial association scheme. Zbl 1063.05135
Caughman, John S.; Maclean, Mark S.; Terwilliger, Paul M.
2005
The displacement and split decompositions for a $$Q$$-polynomial distance-regular graph. Zbl 1065.05097
Terwilliger, Paul
2005
Eigenvalue multiplicities of highly symmetric graphs. Zbl 0495.05045
Terwilliger, Paul
1982
The split decomposition of a tridiagonal pair. Zbl 1127.05108
Nomura, Kazumasa; Terwilliger, Paul
2007
The switching element for a Leonard pair. Zbl 1134.05105
Nomura, Kazumasa; Terwilliger, Paul
2008
Evaluation modules for the $$q$$-tetrahedron algebra. Zbl 1294.17014
Ito, Tatsuro; Rosengren, Hjalmar; Terwilliger, Paul
2014
Finite-dimensional irreducible $$U_q(\mathfrak{sl}_2)$$-modules from the equitable point of view. Zbl 1354.17012
Terwilliger, Paul
2013
Double affine Hecke algebras of rank 1 and the $$\mathbb Z_3$$-symmetric Askey-Wilson relations. Zbl 1220.33018
Ito, Tatsuro; Terwilliger, Paul
2010
The Johnson graph $$J(d,r)$$ is unique if $$(d,r)\neq (2,8)$$. Zbl 0587.05038
Terwilliger, Paul
1986
The determinant of $$AA^{*} - A^{*}A$$ for a Leonard pair $$A,A^{*}$$. Zbl 1108.15007
Nomura, Kazumasa; Terwilliger, Paul
2006
Towards a classification of the tridiagonal pairs. Zbl 1193.05165
Nomura, Kazumasa; Terwilliger, Paul
2008
The Lusztig automorphism of the $$q$$-Onsager algebra. Zbl 1464.17022
Terwilliger, Paul
2018
The $$q$$-Onsager algebra and the positive part of $$U_q(\hat{\mathfrak{sl}}_2)$$. Zbl 1386.17018
Terwilliger, Paul
2017
The $$q$$-Onsager algebra and the universal Askey-Wilson algebra. Zbl 1390.33038
Terwilliger, Paul
2018
Krawtchouk polynomials, the Lie algebra $$\mathfrak{sl}_2$$, and Leonard pairs. Zbl 1261.33001
Nomura, Kazumasa; Terwilliger, Paul
2012
The subconstituent algebra of a distance-regular graph; thin modules with endpoint one. Zbl 1011.05066
Terwilliger, Paul
2002
The Rahman polynomials and the Lie algebra $$\mathfrak{sl}_{3}(\mathbb{C})$$. Zbl 1353.33007
Iliev, Plamen; Terwilliger, Paul
2012
Balanced sets and Q-polynomial association schemes. Zbl 0644.05016
Terwilliger, Paul
1988
Distance-regular graphs of $$q$$-Racah type and the $$q$$-tetrahedron algebra. Zbl 1206.05103
Ito, Tatsuro; Terwilliger, Paul
2009
Distance-regular graphs of $$q$$-Racah type and the universal Askey-Wilson algebra. Zbl 1295.05100
Terwilliger, Paul; Žitnik, Arjana
2014
The classification of finite connected hypermetric spaces. Zbl 0618.05043
Terwilliger, Paul; Deza, Michel
1987
Taut distance-regular graphs and the subconstituent algebra. Zbl 1100.05104
MacLean, Mark S.; Terwilliger, Paul
2006
Distance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra. Zbl 1035.05104
Terwilliger, Paul; Weng, Chih-wen
2004
The subconstituent algebra of a bipartite distance-regular graph; thin modules with endpoint two. Zbl 1136.05076
MacLean, Mark S.; Terwilliger, Paul
2008
The algebra $$U_q(\mathfrak{sl}_2)$$ in disguise. Zbl 1348.17011
2014
An inequality involving the local eigenvalues of a distance-regular graph. Zbl 1047.05045
Terwilliger, Paul
2004
The diameter of bipartite distance-regular graphs. Zbl 0487.05038
Terwilliger, Paul
1982
The Drinfel’d polynomial of a tridiagonal pair. Zbl 1271.15003
Ito, Tatsuro; Terwilliger, Paul
2009
P and Q polynomial schemes with $$q=-1$$. Zbl 0675.05016
Terwilliger, Paul
1987
Tridiagonal pairs and the $$\mu$$-conjecture. Zbl 1155.15011
Nomura, Kazumasa; Terwilliger, Paul
2009
Dual bipartite Q-polynomial distance-regular graphs. Zbl 0921.05064
Dickie, Garth A.; Terwilliger, Paul M.
1996
Billiard arrays and finite-dimensional irreducible $$U_q(\mathfrak{sl}_2)$$-modules. Zbl 1352.17021
Terwilliger, Paul
2014
Tridiagonal pairs of $$q$$-Racah type and the $$\mu$$-conjecture. Zbl 1194.15013
Nomura, Kazumasa; Terwilliger, Paul
2010
The classification of distance-regular graphs of type IIB. Zbl 0727.05050
Terwilliger, P.
1988
The alternating PBW basis for the positive part of $$U_q(\hat{\mathfrak{s} \mathfrak{l}}_2)$$. Zbl 1421.82012
Terwilliger, Paul
2019
The pseudo-cosine sequences of a distance-regular graph. Zbl 1110.05105
Pascasio, Arlene A.; Terwilliger, Paul
2006
Transition maps between the 24 bases for a Leonard pair. Zbl 1169.05055
Nomura, Kazumasa; Terwilliger, Paul
2009
The universal DAHA of type $$(C_1^\vee, C_1)$$ and Leonard pairs of $$q$$-Racah type. Zbl 1371.33031
Nomura, Kazumasa; Terwilliger, Paul
2017
Bipartite $$Q$$-polynomial distance-regular graphs and uniform posets. Zbl 1271.05105
Miklavič, Štefko; Terwilliger, Paul
2013
Using Catalan words and a $$q$$-shuffle algebra to describe a PBW basis for the positive part of $$U_q(\widehat{\mathfrak{sl}}_2)$$. Zbl 1462.17021
Terwilliger, Paul
2019
The quantum adjacency algebra and subconstituent algebra of a graph. Zbl 1416.05142
Terwilliger, Paul; Žitnik, Arjana
2019
The alternating central extension for the positive part of $$U_q(\hat{\mathfrak{sl}}_2)$$. Zbl 1440.81053
Terwilliger, Paul
2019
The $$Q$$-polynomial idempotents of a distance-regular graph. Zbl 1205.05069
Jurišić, Aleksandar; Terwilliger, Paul; Žitnik, Arjana
2010
On the shape of a tridiagonal pair. Zbl 1186.15003
Nomura, Kazumasa; Terwilliger, Paul
2010
Lowering-raising triples and $$U_q(\mathfrak{sl}_2)$$. Zbl 1358.17021
Terwilliger, Paul
2015
A class of distance-regular graphs that are $$\phi$$-polynomial. Zbl 0579.05029
Terwilliger, Paul
1986
$$P$$- and $$\mathcal Q$$-polynomial association schemes and their antipodal $$P$$- polynomial covers. Zbl 0779.05058
Terwilliger, Paul
1993
Leonard pairs, spin models, and distance-regular graphs. Zbl 1448.05064
Nomura, Kazumasa; Terwilliger, Paul
2021
A conjecture concerning the $$q$$-Onsager algebra. Zbl 07407248
Terwilliger, Paul
2021
The alternating central extension of the $$q$$-Onsager algebra. Zbl 07424944
Terwilliger, Paul
2021
Tridiagonal pairs of $$q$$-Racah-type and the $$q$$-tetrahedron algebra. Zbl 1481.17025
Terwilliger, Paul
2021
Idempotent systems. Zbl 07357258
Nomura, Kazumasa; Terwilliger, Paul
2021
The Norton algebra of a $$Q$$-polynomial distance-regular graph. Zbl 1479.05372
Terwilliger, Paul
2021
Totally bipartite tridiagonal pairs. Zbl 07373356
Nomura, Kazumasa; Terwilliger, Paul
2021
An infinite-dimensional $$\square_q$$-module obtained from the $$q$$-shuffle algebra for affine $$\mathfrak{sl}_2$$. Zbl 07196494
Post, Sarah; Terwilliger, Paul
2020
The alternating PBW basis for the positive part of $$U_q(\hat{\mathfrak{s} \mathfrak{l}}_2)$$. Zbl 1421.82012
Terwilliger, Paul
2019
Using Catalan words and a $$q$$-shuffle algebra to describe a PBW basis for the positive part of $$U_q(\widehat{\mathfrak{sl}}_2)$$. Zbl 1462.17021
Terwilliger, Paul
2019
The quantum adjacency algebra and subconstituent algebra of a graph. Zbl 1416.05142
Terwilliger, Paul; Žitnik, Arjana
2019
The alternating central extension for the positive part of $$U_q(\hat{\mathfrak{sl}}_2)$$. Zbl 1440.81053
Terwilliger, Paul
2019
Self-dual Leonard pairs. Zbl 1454.15010
Nomura, Kazumasa; Terwilliger, Paul
2019
The Lusztig automorphism of the $$q$$-Onsager algebra. Zbl 1464.17022
Terwilliger, Paul
2018
The $$q$$-Onsager algebra and the universal Askey-Wilson algebra. Zbl 1390.33038
Terwilliger, Paul
2018
An action of the free product $$\mathbb{Z}_2 \star \mathbb{Z}_2 \star \mathbb{Z}_2$$ on the $$q$$-Onsager algebra and its current algebra. Zbl 1400.81123
Terwilliger, Paul
2018
Tridiagonal pairs of $$q$$-Racah type, the Bockting operator {$$\psi$$}, and $$L$$-operators for $$U_{q}(L(\mathfrak{sl}_{2}))$$. Zbl 1426.17011
Terwilliger, Paul
2018
A poset $$\Phi_{n}$$ whose maximal chains are in bijection with the $$n\times n$$ alternating sign matrices. Zbl 1392.05021
Terwilliger, Paul
2018
The $$q$$-Onsager algebra and the positive part of $$U_q(\hat{\mathfrak{sl}}_2)$$. Zbl 1386.17018
Terwilliger, Paul
2017
The universal DAHA of type $$(C_1^\vee, C_1)$$ and Leonard pairs of $$q$$-Racah type. Zbl 1371.33031
Nomura, Kazumasa; Terwilliger, Paul
2017
The Lusztig automorphism of $$U_q(\mathfrak{sl}_2)$$ from the equitable point of view. Zbl 1386.17019
Terwilliger, Paul
2017
Leonard triples of $$q$$-Racah type and their pseudo intertwiners. Zbl 1352.15015
Terwilliger, Paul
2017
Lowering-raising triples and $$U_q(\mathfrak{sl}_2)$$. Zbl 1358.17021
Terwilliger, Paul
2015
Evaluation modules for the $$q$$-tetrahedron algebra. Zbl 1294.17014
Ito, Tatsuro; Rosengren, Hjalmar; Terwilliger, Paul
2014
Distance-regular graphs of $$q$$-Racah type and the universal Askey-Wilson algebra. Zbl 1295.05100
Terwilliger, Paul; Žitnik, Arjana
2014
The algebra $$U_q(\mathfrak{sl}_2)$$ in disguise. Zbl 1348.17011
2014
Billiard arrays and finite-dimensional irreducible $$U_q(\mathfrak{sl}_2)$$-modules. Zbl 1352.17021
Terwilliger, Paul
2014
The universal Askey-Wilson algebra and DAHA of type $$(C_{1}^{\vee },C_{1})$$. Zbl 1293.33022
Terwilliger, Paul
2013
Finite-dimensional irreducible $$U_q(\mathfrak{sl}_2)$$-modules from the equitable point of view. Zbl 1354.17012
Terwilliger, Paul
2013
Bipartite $$Q$$-polynomial distance-regular graphs and uniform posets. Zbl 1271.05105
Miklavič, Štefko; Terwilliger, Paul
2013
Augmented down-up algebras and uniform posets. Zbl 1310.06003
Terwilliger, Paul; Worawannotai, Chalermpong
2013
Krawtchouk polynomials, the Lie algebra $$\mathfrak{sl}_2$$, and Leonard pairs. Zbl 1261.33001
Nomura, Kazumasa; Terwilliger, Paul
2012
The Rahman polynomials and the Lie algebra $$\mathfrak{sl}_{3}(\mathbb{C})$$. Zbl 1353.33007
Iliev, Plamen; Terwilliger, Paul
2012
The universal Askey-Wilson algebra. Zbl 1244.33015
Terwilliger, Paul
2011
The universal Askey-Wilson algebra and the equitable presentation of $$U_{q}(sl_{2})$$. Zbl 1244.33016
Terwilliger, Paul
2011
A classification of sharp tridiagonal pairs. Zbl 1225.15015
Ito, Tatsuro; Nomura, Kazumasa; Terwilliger, Paul
2011
The equitable basis for $${\mathfrak{sl}_2}$$. Zbl 1277.17013
Benkart, Georgia; Terwilliger, Paul
2011
Tridiagonal matrices with nonnegative entries. Zbl 1219.15023
Nomura, Kazumasa; Terwilliger, Paul
2011
Mock tridiagonal systems. Zbl 1233.15003
Ito, Tatsuro; Terwilliger, Paul
2011
The augmented tridiagonal algebra. Zbl 1236.17022
Ito, Tatsuro; Terwilliger, Paul
2010
Double affine Hecke algebras of rank 1 and the $$\mathbb Z_3$$-symmetric Askey-Wilson relations. Zbl 1220.33018
Ito, Tatsuro; Terwilliger, Paul
2010
Tridiagonal pairs of $$q$$-Racah type and the $$\mu$$-conjecture. Zbl 1194.15013
Nomura, Kazumasa; Terwilliger, Paul
2010
The $$Q$$-polynomial idempotents of a distance-regular graph. Zbl 1205.05069
Jurišić, Aleksandar; Terwilliger, Paul; Žitnik, Arjana
2010
On the shape of a tridiagonal pair. Zbl 1186.15003
Nomura, Kazumasa; Terwilliger, Paul
2010
How to sharpen a tridiagonal pair. Zbl 1237.15012
Ito, Tatsuro; Terwilliger, Paul
2010
Distance-regular graphs with light tails. Zbl 1225.05255
Jurišić, Aleksandar; Terwilliger, Paul; Žitnik, Arjana
2010
An algebra generated by two sets of mutually orthogonal idempotents. Zbl 1239.16027
Ito, Tatsuro; Terwilliger, Paul
2010
Tridiagonal pairs of $$q$$-Racah type. Zbl 1177.33021
Ito, Tatsuro; Terwilliger, Paul
2009
Distance-regular graphs and the $$q$$-tetrahedron algebra. Zbl 1193.17008
Ito, Tatsuro; Terwilliger, Paul
2009
Distance-regular graphs of $$q$$-Racah type and the $$q$$-tetrahedron algebra. Zbl 1206.05103
Ito, Tatsuro; Terwilliger, Paul
2009
The Drinfel’d polynomial of a tridiagonal pair. Zbl 1271.15003
Ito, Tatsuro; Terwilliger, Paul
2009
Tridiagonal pairs and the $$\mu$$-conjecture. Zbl 1155.15011
Nomura, Kazumasa; Terwilliger, Paul
2009
Transition maps between the 24 bases for a Leonard pair. Zbl 1169.05055
Nomura, Kazumasa; Terwilliger, Paul
2009
Finite-dimensional irreducible modules for the three-point $$\mathfrak{sl}_2$$ loop algebra. Zbl 1207.17030
Ito, Tatsuro; Terwilliger, Paul
2008
The structure of a tridiagonal pair. Zbl 1144.05331
Nomura, Kazumasa; Terwilliger, Paul
2008
Sharp tridiagonal pairs. Zbl 1193.05164
Nomura, Kazumasa; Terwilliger, Paul
2008
The switching element for a Leonard pair. Zbl 1134.05105
Nomura, Kazumasa; Terwilliger, Paul
2008
Towards a classification of the tridiagonal pairs. Zbl 1193.05165
Nomura, Kazumasa; Terwilliger, Paul
2008
The subconstituent algebra of a bipartite distance-regular graph; thin modules with endpoint two. Zbl 1136.05076
MacLean, Mark S.; Terwilliger, Paul
2008
Pseudo 1-homogeneous distance-regular graphs. Zbl 1160.05060
Jurišić, Aleksandar; Terwilliger, Paul
2008
Tridiagonal pairs and the quantum affine algebra $$U_q(\widehat{\text{sl}}_2)$$. Zbl 1128.16028
Ito, Tatsuro; Terwilliger, Paul
2007
The tetrahedron algebra, the Onsager algebra, and the $$\mathfrak{sl}_2$$ loop algebra. Zbl 1163.17026
Hartwig, Brian; Terwilliger, Paul
2007
The $$q$$-tetrahedron algebra and its finite dimensional irreducible modules. Zbl 1133.17011
Ito, Tatsuro; Terwilliger, Paul
2007
Two non-nilpotent linear transformations that satisfy the cubic $$q$$-Serre relations. Zbl 1179.17017
Ito, Tatsuro; Terwilliger, Paul
2007
Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair. Zbl 1119.05111
Nomura, Kazumasa; Terwilliger, Paul
2007
Affine transformations of a Leonard pair. Zbl 1143.05337
Nomura, Kazumasa; Terwilliger, Paul
2007
The universal central extension of the three-point $$\mathfrak{sl}_2$$ loop algebra. Zbl 1153.17008
Benkart, Georgia; Terwilliger, Paul
2007
Balanced Leonard pairs. Zbl 1119.05110
Nomura, Kazumasa; Terwilliger, Paul
2007
$$p$$-inverting pairs of linear transformations and the $$q$$-tetrahedron algebra. Zbl 1146.17009
Ito, Tatsuro; Terwilliger, Paul
2007
Tridiagonal pairs of Krawtchouk type. Zbl 1132.15010
Ito, Tatsuro; Terwilliger, Paul
2007
The split decomposition of a tridiagonal pair. Zbl 1127.05108
Nomura, Kazumasa; Terwilliger, Paul
2007
Almost-bipartite distance-regular graphs with the $$Q$$-polynomial property. Zbl 1124.05095
Lang, Michael S.; Terwilliger, Paul M.
2007
An algebraic approach to the Askey scheme of orthogonal polynomials. Zbl 1102.33011
Terwilliger, Paul
2006
The quantum algebra $$U_q(\mathfrak{sl}_2)$$ and its equitable presentation. Zbl 1090.17004
Ito, Tatsuro; Terwilliger, Paul; Weng, Chih-Wen
2006
The equitable presentation for the quantum group associated with a symmetrizable Kac-Moody algebra. Zbl 1106.17021
Terwilliger, Paul
2006
Some trace formulae involving the split sequences of a Leonard pair. Zbl 1085.05070
Nomura, Kazumasa; Terwilliger, Paul
2006
Matrix units associated with the split basis of a Leonard pair. Zbl 1107.05103
Nomura, Kazumasa; Terwilliger, Paul
2006
The determinant of $$AA^{*} - A^{*}A$$ for a Leonard pair $$A,A^{*}$$. Zbl 1108.15007
Nomura, Kazumasa; Terwilliger, Paul
2006
Taut distance-regular graphs and the subconstituent algebra. Zbl 1100.05104
MacLean, Mark S.; Terwilliger, Paul
2006
The pseudo-cosine sequences of a distance-regular graph. Zbl 1110.05105
Pascasio, Arlene A.; Terwilliger, Paul
2006
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array. Zbl 1063.05138
Terwilliger, Paul
2005
Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form. Zbl 1079.15005
Terwilliger, Paul
2005
Two linear transformations each tridiagonal with respect to an eigenbasis of the other: comments on the split decomposition. Zbl 1069.15005
Terwilliger, Paul
2005
The Terwilliger algebra of an almost-bipartite $$P$$- and $$Q$$-polynomial association scheme. Zbl 1063.05135
Caughman, John S.; Maclean, Mark S.; Terwilliger, Paul M.
2005
The displacement and split decompositions for a $$Q$$-polynomial distance-regular graph. Zbl 1065.05097
Terwilliger, Paul
2005
An inequality for regular near polygons. Zbl 1061.05105
Terwilliger, Paul; Weng, Chih-wen
2005
Leonard pairs and the Askey-Wilson relations. Zbl 1062.33018
Terwilliger, Paul; Vidunas, Raimundas
2004
Leonard pairs and the $$q$$-Racah polynomials. Zbl 1075.05090
Terwilliger, Paul
2004
The shape of a tridiagonal pair. Zbl 1037.17013
Ito, Tatsuro; Terwilliger, Paul
2004
Irreducible modules for the quantum affine algebra $$U_{q}(\mathfrak {\widehat{sl}_2})$$ and its Borel subalgebra. Zbl 1106.17014
Benkart, Georgia; Terwilliger, Paul
2004
Distance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra. Zbl 1035.05104
Terwilliger, Paul; Weng, Chih-wen
2004
An inequality involving the local eigenvalues of a distance-regular graph. Zbl 1047.05045
Terwilliger, Paul
2004
Introduction to Leonard pairs. Zbl 1035.05103
Terwilliger, Paul
2003
Leonard pairs from 24 points of view. Zbl 1040.05030
Terwilliger, Paul
2002
Tight distance-regular graphs and the subconstituent algebra. Zbl 1014.05070
Go, Junie T.; Terwilliger, Paul
2002
The subconstituent algebra of a distance-regular graph; thin modules with endpoint one. Zbl 1011.05066
Terwilliger, Paul
2002
Two linear transformations each tridiagonal with respect to an eigenbasis of the other. Zbl 0980.05054
Terwilliger, Paul
2001
Some algebra related to $$P$$- and $$Q$$-polynomial association schemes. Zbl 0995.05148
Ito, Tatsuro; Tanabe, Kenichiro; Terwilliger, Paul
2001
Two relations that generalize the $$q$$-Serre relations and the Dolan-Grady relations. Zbl 1061.16033
Terwilliger, Paul
2001
Tight distance-regular graphs. Zbl 0959.05121
Jurišić, Aleksandar; Koolen, Jack; Terwilliger, Paul
2000
...and 28 more Documents
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### Cited by 352 Authors

 105 Terwilliger, Paul M. 41 Vinet, Luc 37 Nomura, Kazumasa 35 Koolen, Jack H. 30 Hou, Bo 30 Zhedanov, Alexei S. 28 Gao, Suogang 27 Baseilhac, Pascal 24 Ito, Tatsuro 20 Curtin, Brian 20 Miklavič, Štefko 16 Tanaka, Hajime 15 Jurišić, Aleksandar 15 MacLean, Mark S. 14 Huang, Hau-wen 13 Weng, Chih-Wen 12 Crampé, Nicolas 12 Suzuki, Hiroshi 10 Xu, Bangteng 9 Genest, Vincent X. 9 Tsujimoto, Satoshi 8 Alnajjar, Hasan 8 Bannai, Eiichi 8 Hiraki, Akira 7 Bockting-Conrad, Sarah 7 Caughman, John S. IV 7 Deza, Michel Marie 7 Gavrilyuk, Alexander L. 6 Bang, Sejeong 6 Jordan, David Alan 6 Lang, Michael S. 6 Morales, John Vincent S. 6 Pascasio, Arlene A. 6 Penjic, Safet 6 Suda, Sho 5 Bannai, Etsuko 5 Belliard, Samuel 5 Hou, Lihang 5 Kang, Na 5 Laurent, Monique 5 Lee, Jaeho 5 Liang, Xiaoye 5 Makhnëv, Aleksandr Alekseevich 5 Park, Jongyook 5 Žitnik, Arjana 4 Benkart, Georgia M. 4 Bergeron, Geoffroy 4 Funk-Neubauer, Darren 4 Gaboriaud, Julien 4 Iliev, Plamen 4 Kim, Kijung 4 Lu, Ming 4 Martin, William J. 4 Moulton, Vincent L. 4 Neumaier, Arnold 4 Pan, Yeh-jong 4 Tan, Yingying 4 van de Vijver, Wouter 4 Wang, Kaishun 4 Watanabe, Yuta 3 Brouwer, Andries Evert 3 Cantuba, Rafael Reno S. 3 Chen, Xinhong 3 De Bie, Hendrik 3 De Clercq, Hadewijch 3 Godjali, Ali 3 Hanson, Edward 3 Hartwig, Brian 3 Ivanov, Alexander A. 3 Koizumi, Kozo 3 Leanos, Jesus 3 Lv, Benjian 3 Ma, Jianmin 3 Maldonado, Carolina 3 Post, Sarah 3 Samuelson, Peter 3 Sasaki, Ryu 3 Tanaka, Rie 3 Tomiyama, Masato 3 Tsuboi, Zengo 3 Van Dam, Edwin Robert 3 Vanhove, Frédéric 3 Vidali, Janoš 3 Vidunas, Raimundas 3 Vu, Thi Thao 3 Wang, Yan 3 Williford, Jason S. 3 Yang, Yang 3 Yu, Hyonju 2 Avis, David M. 2 Balaji, Srinivasan 2 Berest, Yuri Yu. 2 Blau, Harvey I. 2 Cámara, Marc 2 Coolsaet, Kris 2 Cox, Ben Lewis 2 Daqqa, Ibtisam 2 Dickie, Garth A. 2 Ding, Kequan 2 Egge, Eric S. ...and 252 more Authors
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### Cited in 102 Serials

 109 Linear Algebra and its Applications 61 European Journal of Combinatorics 40 Journal of Algebraic Combinatorics 32 Discrete Mathematics 31 Journal of Algebra 26 Graphs and Combinatorics 22 Journal of Combinatorial Theory. Series B 21 Nuclear Physics. B 18 Journal of Mathematical Physics 18 Journal of Combinatorial Theory. Series A 17 Communications in Algebra 14 The Electronic Journal of Combinatorics 13 Letters in Mathematical Physics 13 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 12 Linear and Multilinear Algebra 9 Communications in Mathematical Physics 9 Journal of Algebra and its Applications 8 Designs, Codes and Cryptography 7 Proceedings of the American Mathematical Society 7 Combinatorica 7 The Ramanujan Journal 6 Transactions of the American Mathematical Society 5 Advances in Mathematics 5 Journal of Computational and Applied Mathematics 5 Ars Mathematica Contemporanea 4 Journal of Pure and Applied Algebra 3 Compositio Mathematica 3 Advances in Applied Mathematics 3 ELA. The Electronic Journal of Linear Algebra 3 Algebras and Representation Theory 3 Annales Henri Poincaré 3 Journal of Statistical Mechanics: Theory and Experiment 2 Discrete Applied Mathematics 2 Journal of Mathematical Analysis and Applications 2 Reviews in Mathematical Physics 2 Acta Applicandae Mathematicae 2 Constructive Approximation 2 Mathematical Programming. Series A. Series B 2 Transformation Groups 2 Doklady Mathematics 2 Journal of Nonlinear Mathematical Physics 2 Proceedings of the Steklov Institute of Mathematics 2 Journal of Physics A: Mathematical and Theoretical 2 Science China. Mathematics 2 Algebraic Combinatorics 1 Indian Journal of Pure & Applied Mathematics 1 Israel Journal of Mathematics 1 Journal of Statistical Physics 1 Mathematical Notes 1 Physics Letters. A 1 Physics Letters. B 1 Reports on Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 Journal of Geometry and Physics 1 Annals of the Institute of Statistical Mathematics 1 Bulletin of the London Mathematical Society 1 Canadian Mathematical Bulletin 1 Colloquium Mathematicum 1 Duke Mathematical Journal 1 Geometriae Dedicata 1 Glasgow Mathematical Journal 1 International Journal of Mathematics and Mathematical Sciences 1 Inventiones Mathematicae 1 Journal of Soviet Mathematics 1 Mathematische Zeitschrift 1 Michigan Mathematical Journal 1 Networks 1 Osaka Journal of Mathematics 1 Siberian Mathematical Journal 1 Studies in Applied Mathematics 1 Bulletin of the Korean Mathematical Society 1 Statistics & Probability Letters 1 Chinese Annals of Mathematics. Series B 1 Acta Mathematicae Applicatae Sinica. English Series 1 Discrete & Computational Geometry 1 Sugaku Expositions 1 International Journal of Mathematics 1 Computational Geometry 1 Expositiones Mathematicae 1 Journal of Knot Theory and its Ramifications 1 The Australasian Journal of Combinatorics 1 Test 1 Applied Categorical Structures 1 Algebra Colloquium 1 St. Petersburg Mathematical Journal 1 Séminaire Lotharingien de Combinatoire 1 Annals of Combinatorics 1 Communications of the Korean Mathematical Society 1 Acta Mathematica Sinica. English Series 1 Communications in Contemporary Mathematics 1 Journal of Applied Mathematics and Computing 1 Algebra and Discrete Mathematics 1 Statistical Methods and Applications 1 The European Physical Journal B. Condensed Matter and Complex Systems 1 International Electronic Journal of Algebra (IEJA) 1 Analysis and Mathematical Physics 1 Arabian Journal of Mathematics 1 Forum of Mathematics, Sigma 1 JSIAM Letters ...and 2 more Serials
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### Cited in 39 Fields

 380 Combinatorics (05-XX) 145 Nonassociative rings and algebras (17-XX) 142 Special functions (33-XX) 98 Linear and multilinear algebra; matrix theory (15-XX) 88 Quantum theory (81-XX) 59 Associative rings and algebras (16-XX) 46 Group theory and generalizations (20-XX) 24 Statistical mechanics, structure of matter (82-XX) 13 Harmonic analysis on Euclidean spaces (42-XX) 12 Geometry (51-XX) 10 Order, lattices, ordered algebraic structures (06-XX) 10 Difference and functional equations (39-XX) 10 Operator theory (47-XX) 10 Information and communication theory, circuits (94-XX) 8 Topological groups, Lie groups (22-XX) 8 Convex and discrete geometry (52-XX) 7 Manifolds and cell complexes (57-XX) 7 Operations research, mathematical programming (90-XX) 6 Algebraic geometry (14-XX) 6 Probability theory and stochastic processes (60-XX) 5 Number theory (11-XX) 5 Commutative algebra (13-XX) 5 Dynamical systems and ergodic theory (37-XX) 3 Functional analysis (46-XX) 3 Numerical analysis (65-XX) 3 Relativity and gravitational theory (83-XX) 2 $$K$$-theory (19-XX) 2 Functions of a complex variable (30-XX) 2 Ordinary differential equations (34-XX) 2 Partial differential equations (35-XX) 2 Differential geometry (53-XX) 2 Algebraic topology (55-XX) 2 Statistics (62-XX) 1 General and overarching topics; collections (00-XX) 1 General algebraic systems (08-XX) 1 Category theory; homological algebra (18-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX)