Zhou, Zhenyu; Xu, Xiaoping Full projective oscillator representations of special linear Lie algebras and combinatorial identities. (English) Zbl 07770092 J. Lie Theory 33, No. 4, 1139-1176 (2023). MSC: 17B10 05A19 PDFBibTeX XMLCite \textit{Z. Zhou} and \textit{X. Xu}, J. Lie Theory 33, No. 4, 1139--1176 (2023; Zbl 07770092) Full Text: arXiv Link
Xu, Xiao Ping Singular conformal oscillator representations of orthosymplectic Lie superalgebras. (English) Zbl 1518.17016 Acta Math. Sin., Engl. Ser. 38, No. 12, 2131-2149 (2022). MSC: 17B10 17B20 22E46 PDFBibTeX XMLCite \textit{X. P. Xu}, Acta Math. Sin., Engl. Ser. 38, No. 12, 2131--2149 (2022; Zbl 1518.17016) Full Text: DOI
Chen, Ling; Xu, Xiaoping Projective oscillator representations of \(sl(n+1|m)\) and \(osp(m|n+1)\). (English) Zbl 1473.17024 Commun. Algebra 49, No. 2, 797-823 (2021). Reviewer: Salah Mehdi (Metz) MSC: 17B10 17B20 PDFBibTeX XMLCite \textit{L. Chen} and \textit{X. Xu}, Commun. Algebra 49, No. 2, 797--823 (2021; Zbl 1473.17024) Full Text: DOI
Xu, Xiaoping Conformal oscillator representations of orthosymplectic Lie superalgebras. (English) Zbl 1495.17012 J. Pure Appl. Algebra 225, No. 3, Article ID 106530, 24 p. (2021). MSC: 17B10 22E46 PDFBibTeX XMLCite \textit{X. Xu}, J. Pure Appl. Algebra 225, No. 3, Article ID 106530, 24 p. (2021; Zbl 1495.17012) Full Text: DOI
Xu, Xiaoping Representations of \(E_7\), equivalent combinatorics and algebraic varieties. (English) Zbl 1422.17015 J. Algebra Appl. 17, No. 3, Article ID 1850045, 22 p. (2018). MSC: 17B10 17B25 22E46 PDFBibTeX XMLCite \textit{X. Xu}, J. Algebra Appl. 17, No. 3, Article ID 1850045, 22 p. (2018; Zbl 1422.17015) Full Text: DOI
Xu, Xiaoping Representations of Lie algebras and partial differential equations. (English) Zbl 1391.17001 Singapore: Springer (ISBN 978-981-10-6390-9/hbk; 978-981-10-6391-6/ebook). xxxvi, 620 p. (2017). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 17-02 17B10 17B22 17B20 PDFBibTeX XMLCite \textit{X. Xu}, Representations of Lie algebras and partial differential equations. Singapore: Springer (2017; Zbl 1391.17001) Full Text: DOI arXiv
Xu, Xiaoping A new functor from \(D_5-\mathrm{Mod}\) to \(E_6-\mathrm{Mod}\). (English) Zbl 1354.17009 Acta Math. Sin., Engl. Ser. 32, No. 8, 867-892 (2016). MSC: 17B20 17B10 17B25 PDFBibTeX XMLCite \textit{X. Xu}, Acta Math. Sin., Engl. Ser. 32, No. 8, 867--892 (2016; Zbl 1354.17009) Full Text: DOI arXiv
Xu, Xiaoping Conformal oscillator representations of orthogonal Lie algebras. (English) Zbl 1375.17008 Sci. China, Math. 59, No. 1, 37-48 (2016). MSC: 17B10 22E46 PDFBibTeX XMLCite \textit{X. Xu}, Sci. China, Math. 59, No. 1, 37--48 (2016; Zbl 1375.17008) Full Text: DOI arXiv
Xu, Xiaoping \(\mathrm{sl}(n+1)\) and \(\mathrm{sp}(2m+2)\). (English) Zbl 1404.17013 J. Lie Theory 26, No. 1, 97-115 (2016). MSC: 17B10 17B20 PDFBibTeX XMLCite \textit{X. Xu}, J. Lie Theory 26, No. 1, 97--115 (2016; Zbl 1404.17013) Full Text: Link
Xu, Xiaoping A new functor from \(E_6\)-Mod to \(E_7\)-Mod. (English) Zbl 1377.17013 Commun. Algebra 43, No. 9, 3589-3635 (2015). MSC: 17B20 17B10 17B25 PDFBibTeX XMLCite \textit{X. Xu}, Commun. Algebra 43, No. 9, 3589--3635 (2015; Zbl 1377.17013) Full Text: DOI arXiv
Xu, Xiao Ping Partial differential equation approach to \(E_7\). (English) Zbl 1353.17008 Acta Math. Sin., Engl. Ser. 31, No. 2, 177-200 (2015). MSC: 17B10 17B25 PDFBibTeX XMLCite \textit{X. P. Xu}, Acta Math. Sin., Engl. Ser. 31, No. 2, 177--200 (2015; Zbl 1353.17008) Full Text: DOI
Luo, Cuiling; Xu, Xiaoping \(\mathbb Z\)-graded oscillator representations of symplectic Lie algebras. (English) Zbl 1308.17011 J. Algebra 403, 401-425 (2014). MSC: 17B10 17B20 PDFBibTeX XMLCite \textit{C. Luo} and \textit{X. Xu}, J. Algebra 403, 401--425 (2014; Zbl 1308.17011) Full Text: DOI
Luo, Cuiling; Xu, Xiaoping \(\mathbb Z\)-graded oscillator generalizations of the classical theorem on harmonic polynomials. (English) Zbl 1286.17009 J. Lie Theory 23, No. 4, 979-1003 (2013). MSC: 17B10 17B20 42B37 PDFBibTeX XMLCite \textit{C. Luo} and \textit{X. Xu}, J. Lie Theory 23, No. 4, 979--1003 (2013; Zbl 1286.17009) Full Text: arXiv Link
Xu, Xiaoping; Zhao, Yufeng Extensions of the conformal representations for orthogonal Lie algebras. (English) Zbl 1292.17008 J. Algebra 377, 97-124 (2013). MSC: 17B10 17B81 PDFBibTeX XMLCite \textit{X. Xu} and \textit{Y. Zhao}, J. Algebra 377, 97--124 (2013; Zbl 1292.17008) Full Text: DOI arXiv Link
Luo, Cuiling; Xu, Xiaoping \(\mathbb Z^2\)-graded oscillator representations of \(\mathrm{sl}(n)\). (English) Zbl 1286.17008 Commun. Algebra 41, No. 8, 3147-3173 (2013). MSC: 17B10 17B20 42B37 PDFBibTeX XMLCite \textit{C. Luo} and \textit{X. Xu}, Commun. Algebra 41, No. 8, 3147--3173 (2013; Zbl 1286.17008) Full Text: DOI
Xu, Xiaoping Differential-operator representations of \(S_n\) and singular vectors in Verma modules. (English) Zbl 1269.17007 Algebr. Represent. Theory 15, No. 2, 211-231 (2012). Reviewer: Volodymyr Mazorchuk (Uppsala) MSC: 17B10 17B20 35A30 35C10 PDFBibTeX XMLCite \textit{X. Xu}, Algebr. Represent. Theory 15, No. 2, 211--231 (2012; Zbl 1269.17007) Full Text: DOI arXiv
Xu, Xiaoping Representations of Lie algebras and coding theory. (English) Zbl 1293.17009 J. Lie Theory 22, No. 3, 647-682 (2012). Reviewer: Michael Wüstner (Schwalbach am Taunus) MSC: 17B10 94B60 17B25 PDFBibTeX XMLCite \textit{X. Xu}, J. Lie Theory 22, No. 3, 647--682 (2012; Zbl 1293.17009) Full Text: arXiv Link
Xu, Xiaoping Partial differential equation approach to \(F_4\). (English) Zbl 1282.17014 Front. Math. China 6, No. 4, 759-774 (2011). MSC: 17B25 17B10 PDFBibTeX XMLCite \textit{X. Xu}, Front. Math. China 6, No. 4, 759--774 (2011; Zbl 1282.17014) Full Text: DOI
Zhao, Yufeng; Xu, Xiaoping Generalized projective representations for \(\mathrm{sl}(n+1)\). (English) Zbl 1261.17007 J. Algebra 328, No. 1, 132-154 (2011). MSC: 17B10 PDFBibTeX XMLCite \textit{Y. Zhao} and \textit{X. Xu}, J. Algebra 328, No. 1, 132--154 (2011; Zbl 1261.17007) Full Text: DOI arXiv
Xu, Xiaoping A cubic \(E_{6}\)-generalization of the classical theorem on harmonic polynomials. (English) Zbl 1253.17009 J. Lie Theory 21, No. 1, 145-164 (2011). MSC: 17B25 17B10 PDFBibTeX XMLCite \textit{X. Xu}, J. Lie Theory 21, No. 1, 145--164 (2011; Zbl 1253.17009) Full Text: Link
Xu, Xiaoping Flag partial differential equations and representations of Lie algebras. (English) Zbl 1171.35343 Acta Appl. Math. 102, No. 2-3, 249-280 (2008). Reviewer: Werner M. Seiler (Kassel) MSC: 35C11 17B30 35G10 17B10 35A30 PDFBibTeX XMLCite \textit{X. Xu}, Acta Appl. Math. 102, No. 2--3, 249--280 (2008; Zbl 1171.35343) Full Text: DOI arXiv
Xu, Xiaoping Tree diagram Lie algebras of differential operators and evolution partial differential equations. (English) Zbl 1134.17005 J. Lie Theory 16, No. 4, 691-718 (2006). MSC: 17B30 35A30 35F15 35G15 35C15 35Q58 PDFBibTeX XMLCite \textit{X. Xu}, J. Lie Theory 16, No. 4, 691--718 (2006; Zbl 1134.17005) Full Text: arXiv Link
Xu, Xiaoping Variational calculus of supervariables and related algebraic structures. (English) Zbl 1012.37048 J. Algebra 223, No. 2, 396-437 (2000). Reviewer: Harry F.Smith (Armidale) MSC: 37K05 37K30 17B80 PDFBibTeX XMLCite \textit{X. Xu}, J. Algebra 223, No. 2, 396--437 (2000; Zbl 1012.37048) Full Text: DOI arXiv
Xu, Xiaoping Differential invariants of classical groups. (English) Zbl 0942.58036 Duke Math. J. 94, No. 3, 543-572 (1998). MSC: 58J70 15A72 22E46 35A30 PDFBibTeX XMLCite \textit{X. Xu}, Duke Math. J. 94, No. 3, 543--572 (1998; Zbl 0942.58036) Full Text: DOI
Xu, Xiaoping Introduction to vertex operator superalgebras and their modules. (English) Zbl 0929.17030 Mathematics and its Applications (Dordrecht). 456. Dordrecht: Kluwer. xvi, 356 p. (1998). Reviewer: Mirko Primc (Zagreb) MSC: 17B69 17-02 94B05 17B67 81R10 PDFBibTeX XMLCite \textit{X. Xu}, Introduction to vertex operator superalgebras and their modules. Dordrecht: Kluwer (1998; Zbl 0929.17030)
Xu, Xiaoping Novikov-Poisson algebras. (English) Zbl 0872.17030 J. Algebra 190, No. 2, 253-279 (1997). Reviewer: I.P.Shestakov (Novosibirsk) MSC: 17D25 17A30 37J99 17B68 17B70 PDFBibTeX XMLCite \textit{X. Xu}, J. Algebra 190, No. 2, 253--279 (1997; Zbl 0872.17030) Full Text: DOI
Xu, Xiaoping Twisted modules of coloured lattice vertex operator superalgebras. (English) Zbl 0857.17024 Q. J. Math., Oxf. II. Ser. 47, No. 186, 233-259 (1996). Reviewer: M.Primc (Zagreb) MSC: 17B69 17B70 PDFBibTeX XMLCite \textit{X. Xu}, Q. J. Math., Oxf. II. Ser. 47, No. 186, 233--259 (1996; Zbl 0857.17024) Full Text: DOI
Xu, Xiaoping Hamiltonian operators and associative algebras with a derivation. (English) Zbl 0837.16034 Lett. Math. Phys. 33, No. 1, 1-6 (1995). MSC: 16W25 37K30 37K10 PDFBibTeX XMLCite \textit{X. Xu}, Lett. Math. Phys. 33, No. 1, 1--6 (1995; Zbl 0837.16034) Full Text: DOI
Xu, Xiaoping Central extensions of self-dual type-A complex lattices. (English) Zbl 0820.17028 Commun. Algebra 22, No. 4, 1281-1303 (1994). Reviewer: K.Abdukhalikov (Almaty) MSC: 17B40 11H56 20D08 20C10 17B69 PDFBibTeX XMLCite \textit{X. Xu}, Commun. Algebra 22, No. 4, 1281--1303 (1994; Zbl 0820.17028) Full Text: DOI