Your browser do not support script. Here are news slide. 研究人員

程舜仁

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Dr. Cheng research interests lie in the representation theory of Lie algebras and Lie superalgebras. His studies in the past include the relationship between the representation theory of classical Lie algebras and that of Lie superalgebras of classical types.  He is especially interested in understanding the characters of modules over Lie superalgebras in general.


Email : chengsj AT math.sinica.edu.tw
Phone:+886 2 2368-5999 ext. 702
Fax: +886 2 2368-9771

著作目錄 :

1.  Representations of central extensions of differentiably simple Lie superalgebras, Communications in Mathematical Physics , 154(1993), no. 3, 555-568
2.  Differentiably simple Lie superalgebras and representations of semisimple Lie superalgebras, Journal of Algebra , 73(1995), no. 1, 1-43
3.  Construction of N=2 Superconformal Algebras from Affine Algebras with Extended Symmetry I, Letters in Mathematical Physics , 33(1995), no. 1, 23-31
4.  Superconformal algebras and Affine Algebras with Extended symmetry, in First International Tainan-Moscow Algebra Workshop, Y. Fong et al eds, de Gruyter, Berlin (1996), 199-206
5.  (with V. G. Kac) A New N=6 Superconformal Algebra, Communications in Mathematical Physics , 186(1997), no. 1, 219-231
6.  (with V. G. Kac) Conformal Modules, Asian Journal of Mathematics , 1(1997), no. 1, 181-193(http://arxiv.org/abs/q-alg/9706030)
7.  (with V. G. Kac, M. Wakimoto) Extensions of conformal modules, in Topological field theory, primitive forms and related topics, M. Kashiwara et al eds., Birkhause, Progress in Mathematics , 160(1998), 79-130(http://arxiv.org/abs/q-alg/9709019)
8.  (with V. G. Kac) Generalized Spencer Cohomology and Filtered Deformations of Z-graded Lie superalgebras, Advances in Theoretical and Mathematical Physics , 2(1998), no. 5, 1141-1182(http://arxiv.org/abs/math/9805039)
9.  (with V. G. Kac) Structure of some Z-graded Lie superalgebras of vectorfields, Transformation Groups , 4(1999), no. 2-3, 219-272
10.  (with V. G. Kac, M. Wakimoto) Extensions of Neveu-Schwarz conformal modules, Journal of Mathematical Physics , 41(2000), no. 4, 2271-2294
11.  (with W. Wang) Remarks on Schur-Howe-Sergeev Duality, Letters in Mathematical Physics , 52(2000), no. 2, 143-153(http://arxiv.org/abs/math/0008109)
12.  (with N. Lam) Finite conformal modules over N=2,3,4 superconformal algebras, Journal of Mathematical Physics , 42(2001), no. 2, 906-933(http://arxiv.org/abs/math/0005274)
13.  (with W. Wang) Howe Duality for Lie Superalgebras, Compositio Mathematica , 128(2001), no. 1, 55-94(http://arxiv.org/abs/math/0008093)
14.  (with W. Wang) Lie Subalgebras of Differential Operators on the Super Circle, Publications of the Research Institute for Mathematical Sciences , 39(2003), no. 3, 545-600(http://arxiv.org/abs/math/0103092)
15.  Gelfand-Tsetlin Pattern and Strict Partitions, Letters in Mathematical Physics , 64(2003), no. 1, 23-30
16.  (with N. Lam) Infinite-dimensional Lie Superalgebras and Hook Schur Functions, Communications in Mathematical Physics , 238(2003), no. 1, 95-118(http://arxiv.org/abs/math/0206034)
17.  (with R. B. Zhang) Analogue of Kostant's u-cohomology Formula for general linear Superalgebra, International Mathematics Research Notices , 2004(2004), no. 1, 31-53
18.  (with R. B. Zhang) Howe Duality and Combinatorial Character Formula for Orthosymplectic Lie Superalgebras, Advances in Mathematics , 182(2004), no. 1, 124-172(http://arxiv.org/abs/math/0206036)
19.  (with W. Wang) The Bloch-Okounkov Correlation Functions at higher Levels, Transformation Groups , 09(2004), no. 2, 133-142(http://arxiv.org/abs/math/0309186)
20.  (with N. Lam , R. B. Zhang) Character Formula for infinite-dimensional unitarizable Modules of the general linear Superalgebra, Journal of Algebra , 273(2004), no. 2, 780-805(http://arxiv.org/abs/math/0301183)
21.  (with W. Wang) The correlation functions of vertex operators and Macdonald polynomials, Journal of Algebraic Combinatorics , 25(2007), no. 1, 43-56
22.  (with W. Wang, R. B. Zhang) A Fock Space Approach to Representation Theory of osp(2|2n), Transformation groups , 12(2007), no. 2, 209-225(http://arxiv.org/abs/math/0510106)
23.  (with D. Taylor, W. Wang) The Bloch-Okounkov Correlation Functions of negative Levels, Journal of Algebra , 319(2008), no. 1, 457-490(http://arxiv.org/abs/0706.3742)
24.  (with J.-H. Kwon, N. Lam) A BGG-type resolution for tensor modules over general linear superalgebra, Letters in Mathematical Physics , 84(2008), no. 1, 75-87(http://arxiv.org/abs/0801.0914)
25.  (with W. Wang, R. B. Zhang) Super Duality and Kazhdan-Lusztig Polynomials, Transactions of the American Mathematical Society , 360(2008), no. 11, 5883-5924(http://arxiv.org/abs/math/0409016)
26.  (with J.-H. Kwon) Howe Duality and Kostant Homology Formula for infinite-dimensional Lie Superalgebras, International Mathematics Research Notices , 2008(2008), no. rnn085, 1-52(http://arxiv.org/abs/0806.2480)
27.  (with W. Wang) Remarks on modules of the ortho-symplectic Lie superalgebras, Bulletin of the Institute of Mathematics Academia Sinica , 3(2008), no. 3, 353-372(http://arxiv.org/abs/0804.2506)
28.  (with W. Wang) Brundan-Kazhdan-Lusztig and Super Duality Conjectures, Publications of the Research Institute for Mathematical Sciences , 44(2008), no. 4, 1219-1272(http://arxiv.org/abs/0705.0050)
29.  (with J.-H. Kwon, W. Wang) Kostant homology formulas for oscillator modules of Lie superalgebras, Advances in Mathematics , 224(2010), no. 4, 1548-1588(http://arxiv.org/abs/0901.0247)
30.  (with N. Lam) Irreducible Characters of General Linear Superalgebra and Super Duality, Communications in Mathematical Physics , 298(2010), no. 3, 645-672(http://arxiv.org/abs/0905.0332)
31.  (with N. Lam, W. Wang) Super duality and irreducible characters of ortho-symplectic Lie superalgebras, Inventiones Mathematicae , 183(2011), no. 1, 189-224(http://arxiv.org/abs/0911.0129)
32.  (with W. Wang) Dualities for Lie superalgebras, Lie Theory and Representation Theory, 1-46, Surveys of Modern Mathematics 2, International Press, Boston, (2012)(http://arxiv.org/abs/1001.0074)
33.  (with N. Lam, W. Wang) Super Duality for General Linear Lie Superalgebras and Applications, Proceedings of Symposia in Pure Mathematics, American Mathematical Society , 86(2012), 113-136(http://arxiv.org/abs/1109.0667)
34.  (with W. Wang) Dualities and Representations of Lie Superalgebras, Graduate Studies in Mathematics 144, American Mathematical Society, 302 pp. ISBN: 978-0-8218-9118-6 (2012), 0-0(http://www.ams.org/bookstore-getitem/item=gsm-144)
35.  (with V. Mazorchuk, W. Wang) Equivalence of blocks for the general linear Lie superalgebra, Letters in Mathematical Physics , 103(2013), no. 12, 1313-1327(http://arxiv.org/abs/1301.1204)
36.  (with J.-H. Kwon, W. Wang) Irreducible characters of Kac-Moody Lie superalgebras, Proceedings of the London Mathematical Society, doi: 10.1112/plms/pdu045 (2014), 0-0(http://arxiv.org/abs/1308.3030)
37.  (with N. Lam, W. Wang) Brundan-Kazhdan-Lusztig conjecture for general linear Lie superalgebras, Duke Mathematical Journal, to appear (2014), 0-0(http://arxiv.org/abs/1203.0092)
38.  (with J.-H. Kwon) Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras, preprint (2014), 0-0(http://arxiv.org/abs/1406.6739)