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# Cheng, Shun-Jen

 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

### Publications :

 1 (with W. Wang) Character formulae in category $\mathcal O$ for exceptional Lie superalgebra $G(3)$, preprint (2018-04) 2 (with Bin Shu, Weiqiang Wang) Modular representations of exceptional supergroups, Mathematische Zeitschrift, to appear (2018-01) 3 (with W. Wang) Character formulae in category $\mathcal O$ for exceptional Lie superalgebras $D(2|1;\zeta)$, Transformation Groups, to appear (2018) 4 Supercharacters of queer Lie superalgebras, Journal of Mathematical Physics , 58(2017), 061701-1-061701-9 5 Representations of central extensions of differentiably simple Lie superalgebras, Communications in Mathematical Physics , 154(1993), no. 3, 555-568 6 Differentiably simple Lie superalgebras and representations of semisimple Lie superalgebras, Journal of Algebra , 73(1995), no. 1, 1-43 7 Construction of N=2 Superconformal Algebras from Affine Algebras with Extended Symmetry I, Letters in Mathematical Physics , 33(1995), no. 1, 23-31 8 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 9 (with V. G. Kac) A New N=6 Superconformal Algebra, Communications in Mathematical Physics , 186(1997), no. 1, 219-231 10 (with V. G. Kac) Conformal Modules, Asian Journal of Mathematics , 1(1997), no. 1, 181-193 11 (with V. G. Kac, M. Wakimoto) Extensions of conformal modules, In: Topological field theory, primitive forms and related topics, M. Kashiwara et al eds., Birkhauser, Progress in Mathematics , 160(1998), 79-130 12 (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 13 (with V. G. Kac) Structure of some Z-graded Lie superalgebras of vectorfields, Transformation Groups , 4(1999), no. 2-3, 219-272 14 (with V. G. Kac, M. Wakimoto) Extensions of Neveu-Schwarz conformal modules, Journal of Mathematical Physics , 41(2000), no. 4, 2271-2294 15 (with W. Wang) Remarks on Schur-Howe-Sergeev Duality, Letters in Mathematical Physics , 52(2000), no. 2, 143-153 16 (with N. Lam) Finite conformal modules over N=2,3,4 superconformal algebras, Journal of Mathematical Physics , 42(2001), no. 2, 906-933 17 (with W. Wang) Howe Duality for Lie Superalgebras, Compositio Mathematica , 128(2001), no. 1, 55-94 18 (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 19 Gelfand-Tsetlin Pattern and Strict Partitions, Letters in Mathematical Physics , 64(2003), no. 1, 23-30 20 (with N. Lam) Infinite-dimensional Lie Superalgebras and Hook Schur Functions, Communications in Mathematical Physics , 238(2003), no. 1, 95-118 21 (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 22 (with R. B. Zhang) Howe Duality and Combinatorial Character Formula for Orthosymplectic Lie Superalgebras, Advances in Mathematics , 182(2004), no. 1, 124-172 23 (with W. Wang) The Bloch-Okounkov Correlation Functions at higher Levels, Transformation Groups , 09(2004), no. 2, 133-142 24 (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 25 (with W. Wang) The correlation functions of vertex operators and Macdonald polynomials, Journal of Algebraic Combinatorics , 25(2007), no. 1, 43-56 26 (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 27 (with D. Taylor, W. Wang) The Bloch-Okounkov Correlation Functions of negative Levels, Journal of Algebra , 319(2008), no. 1, 457-490 28 (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 29 (with W. Wang, R. B. Zhang) Super Duality and Kazhdan-Lusztig Polynomials, Transactions of the American Mathematical Society , 360(2008), no. 11, 5883-5924 30 (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 31 (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 32 (with W. Wang) Brundan-Kazhdan-Lusztig and Super Duality Conjectures, Publications of the Research Institute for Mathematical Sciences , 44(2008), no. 4, 1219-1272 33 (with J.-H. Kwon, W. Wang) Kostant homology formulas for oscillator modules of Lie superalgebras, Advances in Mathematics , 224(2010), no. 4, 1548-1588 34 (with N. Lam) Irreducible Characters of General Linear Superalgebra and Super Duality, Communications in Mathematical Physics , 298(2010), no. 3, 645-672 35 (with N. Lam, W. Wang) Super duality and irreducible characters of ortho-symplectic Lie superalgebras, Inventiones Mathematicae , 183(2011), no. 1, 189-224 36 (with W. Wang) Dualities for Lie superalgebras, Lie Theory and Representation Theory, In: Surveys of Modern Mathematics 2, International Press, Boston (2012), 1-46 37 (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 38 (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 39 (with V. Mazorchuk, W. Wang) Equivalence of blocks for the general linear Lie superalgebra, Letters in Mathematical Physics , 103(2013), no. 12, 1313-1327 40 (with J.-H. Kwon, W. Wang) Irreducible characters of Kac-Moody Lie superalgebras, Proceedings of the London Mathematical Society , 110(2015), no. 1, 108-132 41 (with N. Lam, W. Wang) Brundan-Kazhdan-Lusztig conjecture for general linear Lie superalgebras, Duke Mathematical Journal , 164(2015), no. 4, 617-695 42 (with J.-H. Kwon) Finite-dimensional half-integer weight modules over queer Lie superalgebras, Communications in Mathematical Physics , 346(2016), 945-965 43 (with J.-H. Kwon) Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras, Advances in Mathematics , 304(2017), 1296-1329 44 (with C.-W. Chen) Quantum group of type $A$ and representations of queer Lie superalgebra, Journal of Algebra , 473(2017), 1-28 45 (with J.-H. Kwon and W. Wang) Character formulae for queer Lie superalgebras and canonical bases of types $A/C$, Communications in Mathematical Physics , 352(2017), 1091-1119