Distinguished Research Fellow |   Cheng, Shun-Jen
Contact Information
• chengsj$\color{red}{@}$math.sinica.edu.tw
• +886 2 2368-5999 ext. 702
• +886 2 2368-9771
Research Interests
• Lie algebras
• Lie superalgebras
• Representation Theory
Education
• Ph.D. in Mathematics, A.M. in Mathematics Harvard University (1988 – 1993)
• B.A. in Mathematics (with highest distinction), M.S. in Mathematics Northwestern University (1984 –1988)

Work Experience
• Acting Director Institute of Mathematics Academia Sinica 2018/8-2020/4
• Director Institute of Mathematics Academia Sinica 2015/8-2018/8
• Acting Director Institute of Mathematics Academia Sinica 2013/8 - 2015/8
• Distinguished Research Fellow Academia Sinica 2013/4 - present
• Deputy Director Institute of Mathematics Academia Sinica 2011/4 - 2013/8
• Joint Appointment Professor National Taiwan University 2006/8 - present
• Research Fellow Academia Sinica 2006/8 - 2013/3
• Visiting Professor University of Virginia 2003/8 - 2004/7
• Professor National Taiwan University 2000/8 - 2006/7
• Professor National Cheng-Kung University 1998/8 - 2000/7
• Visiting Scholar Massachusetts Institute of Technology 1997/9 - 1998/8
• Associate Professor National Cheng-Kung University 1994/8 - 1998/7
• Visiting Member Max-Planck-Institut für Mathematik 1993/10 – 1994/9

Awards
• Academic Award of the Ministry of Education, 2011
• The World Academy of Sciences TWAS Prize in Mathematics, 2011
• Khwarizmi International Award, 2010
• Academia Sinica Investigator Awards, 2007, 2014
• Academia Sinica Research Award for Junior Research Investigators, 1999
• National Science Council Outstanding Research Awards, 1997-1998, 1999-2000, 2011–2013

Research Descriptions

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.

Selected Publications
1. (with C.-W. Chen) "Whittaker categories of quasi-reductive Lie superalgebras and quantum symmetric pairs" , preprint , 2022-08.
2. (with C.-W. Chen, V. Mazorchuk) "Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras" , preprint , 2022-03.
3. (with C.-W. Chen, K. Coulembier) "Tilting modules for classical Lie superalgebras" , Journal of London Mathematical Society , 103 (2), 870-900, 2021-4.
4. (with C.-W. Chen, L. Luo) "Blocks and characters of $G(3)$-modules of non-integral weights" , Journal of Algebra , 588, 574-616, 2021-12.
5. (with K. Coulembier) "Representation theory of a semisimple extension of the Takiff superalgebra" , International Mathematics Research Notices, to appear , 2021-05.
6. (with C.-W. Chen, L. Luo) "Blocks and characters of $D(2|1;\zeta)$-modules of non-integral weights" , Transformation Groups, to appear , 2021-04.
7. (with B. Shu, W. Wang) "Modular representations of exceptional supergroups" , Mathematische Zeitschrift , 219 (2), 635-659, 2019-03.
8. (with W. Wang) "Character formulae in category $\mathcal O$ for exceptional Lie superalgebras $D(2|1;\zeta)$" , Transformation Groups , 24 (3), 781-821, 2019.
9. (with W. Wang) "Character formulae in category $\mathcal O$ for exceptional Lie superalgebra $G(3)$" , Kyoto Journal of Mathematics, to appear , 2018-10.
10. "Supercharacters of queer Lie superalgebras" , Journal of Mathematical Physics , 58, 061701-1-061701-9, 2017.
11. (with C.-W. Chen) "Quantum group of type $A$ and representations of queer Lie superalgebra" , Journal of Algebra , 473, 1-28, 2017.
12. (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, 1091-1119, 2017.
13. (with J.-H. Kwon) "Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras" , Advances in Mathematics , 304, 1296-1329, 2017.
14. (with J.-H. Kwon) "Finite-dimensional half-integer weight modules over queer Lie superalgebras" , Communications in Mathematical Physics , 346, 945-965, 2016.
15. (with J.-H. Kwon, W. Wang) "Irreducible characters of Kac-Moody Lie superalgebras" , Proceedings of the London Mathematical Society , 110 (1), 108-132, 2015.
16. (with N. Lam, W. Wang) "Brundan-Kazhdan-Lusztig conjecture for general linear Lie superalgebras" , Duke Mathematical Journal , 164 (4), 617-695, 2015.
17. (with V. Mazorchuk, W. Wang) "Equivalence of blocks for the general linear Lie superalgebra" , Letters in Mathematical Physics , 103 (12), 1313-1327, 2013.
18. (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.
19. (with N. Lam, W. Wang) "Super Duality for General Linear Lie Superalgebras and Applications" , Proceedings of Symposia in Pure Mathematics, American Mathematical Society , 86, 113-136, 2012.
20. (with W. Wang) "Dualities for Lie superalgebras, Lie Theory and Representation Theory" , In: Surveys of Modern Mathematics 2, International Press, Boston , 1-46, 2012.
21. (with N. Lam, W. Wang) "Super duality and irreducible characters of ortho-symplectic Lie superalgebras" , Inventiones Mathematicae , 183 (1), 189-224, 2011.
22. (with N. Lam) "Irreducible Characters of General Linear Superalgebra and Super Duality" , Communications in Mathematical Physics , 298 (3), 645-672, 2010.
23. (with J.-H. Kwon, W. Wang) "Kostant homology formulas for oscillator modules of Lie superalgebras" , Advances in Mathematics , 224 (4), 1548-1588, 2010.
24. (with J.-H. Kwon, N. Lam) "A BGG-type resolution for tensor modules over general linear superalgebra" , Letters in Mathematical Physics , 84 (1), 75-87, 2008.
25. (with W. Wang) "Remarks on modules of the ortho-symplectic Lie superalgebras" , Bulletin of the Institute of Mathematics Academia Sinica , 3 (3), 353-372, 2008.
26. (with W. Wang) "Brundan-Kazhdan-Lusztig and Super Duality Conjectures" , Publications of the Research Institute for Mathematical Sciences , 44 (4), 1219-1272, 2008.
27. (with J.-H. Kwon) "Howe Duality and Kostant Homology Formula for infinite-dimensional Lie Superalgebras" , International Mathematics Research Notices , 2008 (rnn085), 1-52, 2008.
28. (with D. Taylor, W. Wang) "The Bloch-Okounkov Correlation Functions of negative Levels" , Journal of Algebra , 319 (1), 457-490, 2008.
29. (with W. Wang, R. B. Zhang) "Super Duality and Kazhdan-Lusztig Polynomials" , Transactions of the American Mathematical Society , 360 (11), 5883-5924, 2008.
30. (with W. Wang) "The correlation functions of vertex operators and Macdonald polynomials" , Journal of Algebraic Combinatorics , 25 (1), 43-56, 2007.
31. (with W. Wang, R. B. Zhang) "A Fock Space Approach to Representation Theory of osp(2|2n)" , Transformation groups , 12 (2), 209-225, 2007.
32. (with N. Lam , R. B. Zhang) "Character Formula for infinite-dimensional unitarizable Modules of the general linear Superalgebra" , Journal of Algebra , 273 (2), 780-805, 2004.
33. (with R. B. Zhang) "Howe Duality and Combinatorial Character Formula for Orthosymplectic Lie Superalgebras" , Advances in Mathematics , 182 (1), 124-172, 2004.
34. (with R. B. Zhang) "Analogue of Kostant's u-cohomology Formula for general linear Superalgebra" , International Mathematics Research Notices , 2004 (1), 31-53, 2004.
35. (with W. Wang) "The Bloch-Okounkov Correlation Functions at higher Levels" , Transformation Groups , 09 (2), 133-142, 2004.
36. "Gelfand-Tsetlin Pattern and Strict Partitions" , Letters in Mathematical Physics , 64 (1), 23-30, 2003.
37. (with W. Wang) "Lie Subalgebras of Differential Operators on the Super Circle" , Publications of the Research Institute for Mathematical Sciences , 39 (3), 545-600, 2003.
38. (with N. Lam) "Infinite-dimensional Lie Superalgebras and Hook Schur Functions" , Communications in Mathematical Physics , 238 (1), 95-118, 2003.
39. (with W. Wang) "Howe Duality for Lie Superalgebras" , Compositio Mathematica , 128 (1), 55-94, 2001.
40. (with N. Lam) "Finite conformal modules over N=2,3,4 superconformal algebras" , Journal of Mathematical Physics , 42 (2), 906-933, 2001.
41. (with W. Wang) "Remarks on Schur-Howe-Sergeev Duality" , Letters in Mathematical Physics , 52 (2), 143-153, 2000.
42. (with V. G. Kac, M. Wakimoto) "Extensions of Neveu-Schwarz conformal modules" , Journal of Mathematical Physics , 41 (4), 2271-2294, 2000.
43. (with V. G. Kac) "Structure of some Z-graded Lie superalgebras of vectorfields" , Transformation Groups , 4 (2-3), 219-272, 1999.
44. (with V. G. Kac) "Generalized Spencer Cohomology and Filtered Deformations of Z-graded Lie superalgebras" , Advances in Theoretical and Mathematical Physics , 2 (5), 1141-1182, 1998.
45. (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, 79-130, 1998.
46. (with V. G. Kac) "Conformal Modules" , Asian Journal of Mathematics , 1 (1), 181-193, 1997.
47. (with V. G. Kac) "A New N=6 Superconformal Algebra" , Communications in Mathematical Physics , 186 (1), 219-231, 1997.
48. "Superconformal algebras and Affine Algebras with Extended symmetry" , In: First International Tainan-Moscow Algebra Workshop, Y. Fong et al eds, de Gruyter, Berlin , 199-206, 1996.
49. "Construction of N=2 Superconformal Algebras from Affine Algebras with Extended Symmetry I" , Letters in Mathematical Physics , 33 (1), 23-31, 1995.
50. "Differentiably simple Lie superalgebras and representations of semisimple Lie superalgebras" , Journal of Algebra , 73 (1), 1-43, 1995.
51. "Representations of central extensions of differentiably simple Lie superalgebras" , Communications in Mathematical Physics , 154 (3), 555-568, 1993.