I have research interests in the following subjects:

 

·      Quantum groups, quantum symmetric pairs, and canonical bases

·      Hecke algebras: finite, affine, and degenerate/spin variants

·      (Spin) symmetric groups and algebraic q-combinatorics

·      Infinite-dimensional Lie algebras and vertex algebras

·      (Super) category O and Kazhdan-Lusztig theory

·      Representation theory of Lie superalgebras

·    Geometric representation theory

·      Modular representation theory

·      Categorification

    (More keywords: Schur duality, Howe duality, super duality, McKay correspondence, Hilbert schemes of points)

 

My papers in arXiv


Books


(a) Research Monographs

    1.  A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs, (with H. Bao), Asterisque 402, 2018, vii+134pp.
        arxiv:1310.0103v2

    2.  Affine flag varieties and quantum symmetric pairs. (with Z. Fan, C. Lai, Y. Li, L. Luo). Memoirs AMS (to appear), 113pp. 
        arxiv:1602.04383
 

(b) Textbooks 

     Dualities and Representations of Lie Superalgebras. (with S.-J. Cheng).  Graduate Studies in Mathematics 144, AMS, 2012, xi+302pp.

(c) Conference proceedings

     1. Proceedings for conference on representation theory (in honor of Lusztig’s 70th birthday, 2016). (Edited with S.-J. Cheng and D. Vogan). Bulletin of Inst. of Math. Academia Sinica, vol. 13, 2018, iv+363 pp.

     2.  Geometric representation theory and extended affine Lie algebras. (Edited with E. Neher, A. Savage). Fields Institute Communications 59, 2011, viii+213pp.

     3.  Infinite-dimensional aspects of representation theory and applications. (Edited with S. Berman, B. Parshall, L. Scott). Contemporary Mathematics 392, AMS, 2005, viii+154pp.

 


Preprints

  1. Quantum Supergroups VI. Roots of 1, (with Chris Chung and Thomas Sale), 21 pages
  2. A Serre presentation for the i-quantum groups, (with Xinhong Chen and Ming Lu), 28 pages
    arxiv:1810.12475
  3. Addendum to ``Canonical bases arising from quantum symmetric pairs”, (with H. Bao and H. Watanabe), 9 pages
    arxiv:1808.09388
  4. Formulae for i-divided powers in U_q(sl_2), II, (with C. Berman), 50 pages
    arxiv:1806.00878
  5. Stability of the centers of group algebras of GL_n(q), (with Jinkui Wan), 31 pages
    arxiv:1805.08796
  6. Anti-commuting varieties, (with Xinhong Chen), 26 pages
    arxiv:180
    5.00378
  7. Character formulae in category O for exceptional Lie superalgebra G(3),  (with S.-J. Cheng), 28 pages
    arxiv:1804.06951
  8. Quantum Schur duality of affine type C with three parameters, (with Z. Fan,  C. Lai,  Y. Li,  L. Luo,  H. Watanabe), 24 pages
    arxiv:1802.01047
  9. The q-Schur algebras and q-Schur dualities of finite type, (with Li Luo), 32 pages
    arxiv:1710.10375
  10. Affine Hecke algebras and quantum symmetric pairs, (with Z. Fan,  C. Lai,  Y. Li,  L. Luo), 87 pages
    arxiv:1609.06199
    v2
  11. *Hilbert schemes, wreath products, and the McKay correspondence, 29 page, 1999 (*unpublished)
    arxiv:math/9912104

 

Papers accepted

  1. Modular representations of exceptional supergroups, (with S.-J. Cheng and B. Shu), Math. Z.
    arxiv:1801.05
    077
  2. Character formulae in category O for exceptional Lie superalgebras D(2|1;a),  (with S.-J. Cheng),  Transform. Groups
    arxiv:1704.00846

Papers published 


2018

         93. Categorification of quantum symmetric pairs I, (with H. Bao, P. Shan, B. Webster), Quantum Topol. 9 (2018), 643-714

               arxiv:1605.03780 

         92. Canonical bases arising from quantum symmetric pairs, (with H. Bao), Inventiones Math. 213 (2018), 1099-1177

               arxiv:1610.09271v2 

         91. Geometric Schur duality of classical type, (with H. Bao, J. Kujawa, Y. Li),  [Appendix with H. Bao, Y. Li], Transform. Groups 23 (2018), 329-389

               arxiv:1404.4000 

         90. Multiparameter quantum Schur duality of type B, (with H. Bao and H. Watanabe), Proc. AMS 146 (2018), 3203-3216

               arxiv:1609.01766 

         89. Formulae for i-divided powers in U_q(sl_2), (with C. Berman), J. Pure Appl. Algebra 222 (2018), 2667-2702

               arxiv:1703.00602

         88. Positivity vs negativity of canonical bases, (with Y.  Li),  Proceedings for Lusztig’s 70th birthday conference,  Bulletin of Institute of Mathematics Academia Sinica (N.S.) 13 (2018), 143-198

               arxiv:1501.00688

         87. Some conjectures on modular representations of affine sl_2 and Virasoro algebra,   Science China Math.  61 (2018), 385-390
               arxiv:1608.07896

         86.   Spin nilHecke algebras of classical type, (with I. Johnson),  J. Algebra 487 (2018), 19-54
               arxiv:1706.06240

 2017

         85.    Character formulae for queer Lie superalgebras and canonical bases of types A/C, (with S.-J. Cheng and J.-H. Kwon),  Commun. Math. Phys. 352 (2017), 1091-1119

              arxiv:1512.00116

2016

         84.    Modular affine vertex algebras and baby Wakimoto modules, (with T. Arakawa), Proc. Symp. Pure Math.  92 (2016),  1-15

    arxiv:1503.00395

83.    Canonical bases in tensor products revisited, (with H. Bao), Amer. J. Math.  138 (2016), 1731-1738

    arxiv:1403.0039

82.    Quantum shuffles and quantum supergroups of basic type, (with S. Clark and D. Hill), Quantum Topology 7 (2016), 553-638

              arxiv:1310.7523v3

2015

81.    Frobenius map for the centers of Hecke algebras, (with Jinkui Wan), Trans. Amer. Math. Soc. 367 (2015), 5507-5520

    arxiv:1208.4446

80.    Brundan-Kazhdan-Lusztig conjecture for general linear Lie superalgebras, (with Shun-Jen Cheng and Ngau Lam), Duke Math. J. 164 (2015), 617-695

    arxiv:1203.0092

79.    Coinvariant algebras and fake degrees for spin Weyl groups of exceptional type, (with Constance Baltera), J. Algebra 442 (2015), 66-79

    arxiv:1306.1290

78.    Irreducible characters for Kac-Moody Lie superalgebras, (with S.-J. Cheng and J.-H. Kwon),  Proc. London Math. Soc. 110 (2015) 108-132

    arxiv:1308.3030

77.    Categorification of quantum Kac-Moody superalgebras, (with D. Hill), Trans. Amer. Math. Soc. 367 (2015), 1183-1216

    arxiv:1202.2769

2014

76.  Quantum supergroups II. Canonical basis, (with S. Clark and D. Hill), Represent. Theory 18 (2014), 278-309

    arxiv:1304.7837

75.  Quantum supergroups III. Twistors,  (with S. Clark, Z. Fan, and Y. Li),  Commun. Math. Phys. 332 (2014), 415-436

    arxiv:1307.7056

74.  Coinvariant algebras and fake degrees for spin Weyl groups of classical type, (with Constance Baltera), Math. Proc. Cambridge Philos. Soc. 156 (2014), 43-79 

    arxiv:1207.0525v2 

2013

73.  Quantum supergroups I. Foundations, (with S. Clark and D. Hill), Transform. Groups  18 (2013), 1019-1053

     arxiv:1301.1665

72.  Equivalence of blocks for the general linear Lie superalgebra, (with S.-J. Cheng and V. Mazorchuk), Lett. Math. Phys. 103 (2013), 1313-1327

     arxiv:1301.1204

71.  Canonical basis for quantum osp(1|2), (with Sean Clark), Lett. Math. Phys. 103 (2013), 207-231

     arxiv:1204.3940

70.  Frobenius character formula and spin generic degrees of Hecke-Clifford algebras, (with Jinkui Wan), Proc. London Math. Soc. 106 (2013), 287-317

     arxiv:1201.2457

69.  Spin Kostka polynomials, (with Jinkui Wan), J. Algebr. Comb. 37 (2013), 117-138,

     arxiv:1102.4901  

2012

68.  Super duality for general linear Lie superalgebras and applications, (with Shun-Jen Cheng and Ngau Lam), Proc. Symp. Pure Math. 86 (2012), 113-136

     arxiv:1109.0667

67.  Lectures on spin representation theory of symmetric groups, (with Jinkui Wan), In: Proceedings for Taipei winter school 2010, Bulletin of Institute of Mathematics Academia Sinica (N.S.) 7 (2012), 91-164

     arxiv:1110.0263 

2011

66.  The GL_n(q)-module structure of the symmetric algebra around the Steinberg module, (with Jinkui Wan), Adv. in Math. 227 (2011), 1562-1584

     arxiv:1012.0406

65.  Twisted Dickson-Mui invariants and the Steinberg module multiplicity, (with Jinkui Wan), Math. Proc. Cambridge Philos. Soc. 151 (2011), 43-57

     arxiv:1009.0414

64.  Representations of Lie superalgebras in prime characteristic II: The queer series, (with Lei Zhao), J. Pure Applied Algebra 215 (2011), 2515-2532

     arxiv:0902.2758

63.  Spin invariant theory for the symmetric group, (with Jinkui Wan), J. Pure Applied Algebra 215 (2011), 1569-1581

     arxiv:1002.0272

62.  Super duality and irreducible characters of ortho-symplectic Lie superalgebras, (with Shun-Jen Cheng and Ngau Lam), Invent. Math. 183 (2011), 189-224

     arxiv:0911.0129

61.  Graded Specht modules, (with J. Brundan and A. Kleshchev), J. reine angew. Math. 655 (2011), 61-87

     arxiv:0901.0218

60.  Nilpotent orbits and finite W-algebras, in Geometric Representation Theory and Extended Affine Lie Algebras, Fields Institute Communications 59 (Eds. E. Neher, A. Savage, W. Wang), AMS, Providence, RI, 2011, pp. 71-105

     arxiv:0912.0689

59.  Dualities for Lie superalgebras, (with Shun-Jen Cheng), Lectures for Shanghai summer school 2009, Surveys of Modern Mathematics 2 (2011), 1-46

     arxiv:1001.0074

2010

58.  Kostant homology formulas for oscillator modules of Lie superalgebras, (with S.-J. Cheng and J.-H. Kwon), Adv. Math. 224 (2010), 1548-1588

     arxiv:0901.0247 

2009

57.  Double affine Hecke algebras for the spin symmetric group, Math. Res. Lett. 16 (2009), 1071-1085

     arxiv:math/0608074

56.  Representations of Lie superalgebras in prime characteristic I, (with Lei Zhao), Proc. London Math. Soc. 99 (2009), 145-167

     arxiv:0808.0046

55.  Hecke-Clifford algebras and spin Hecke algebras IV: odd double affine type, (with Ta Khongsap), SIGMA  5 (2009), 012, 27 pages

     arxiv:0810.2068

54.  The centers of Iwahori-Hecke algebras are filtered, (with Andrew Francis), Contemp. Math. 478 (2009), 29-37

     arxiv:0803.3361

53.  The centers of spin symmetric group algebras and Catalan numbers, (with Jill Tysse), J. Algebr. Combin. 29 (2009), 175-193

     arxiv:0711.3054

2008

52.  Modular representations and branching rules for wreath Hecke algebras, (with Jinkui Wan), IMRN (2008), Article ID: rnn128-31, 31 pages

     arxiv:0806.0196

51.  Brundan-Kazhdan-Lusztig and super duality conjectures, (with Shun-Jen Cheng), Publ. RIMS 44 (2008), 1219-1272

     arxiv:0705.0050

50.  Hecke-Clifford algebras and spin Hecke algebras II: the rational double affine type, (with Ta Khongsap), Pacific J. Math. 238 (2008), 73-103

     arxiv:0710.5877

49.  Remarks on modules of the ortho-symplectic Lie superalgebras, (with Shun-Jen Cheng), Bulletin of Inst. of Math Academia Sinica (N.S.) 3 (2008), 353-372

     arxiv:0804.2506

48.  Hecke-Clifford algebras and spin Hecke algebras I: the classical affine type, (with Ta Khongsap), Transformation Groups 13 (2008), 389-412

     arxiv:0704.0201

47.  Super duality and Kazhdan-Lusztig polynomials, (with S.-J. Cheng and R.B.~Zhang), Trans. AMS 360 (2008), 5883-5924

     arxiv:math/0409016

46.  The Bloch-Okounkov correlation functions of negative level, (with S.-J. Cheng and David Taylor), J. Algebra 319 (2008), 457-490

     arxiv:0706.3742

45.  Modular representations of the ortho-symplectic supergroups, (with Bin Shu), Proc. London Math. Soc. 96 (2008), 251-271

     arxiv:0706.0348

2007

44.  Spin Hecke algebras of finite and affine types, Adv. in Math. 212 (2007), 723-748

     arXiv:math/0611950

43.  The Bloch-Okounkov correlation functions of classical type, (with Dave Taylor), Commun. Math. Phys.  276 (2007), 473-508

     arXiv:math/0609036

42.  The correlation functions of vertex operators and Macdonald polynomials, (with S.-J. Cheng), J. Algebraic Combin. 25 (2007), 43-56

     arXiv:math/0512064

41.  A Fock space approach to representation theory of  osp(2|2n),  (with S.-J. Cheng and R.B. Zhang), Transform. Groups  12 (2007), 209-225

     arXiv:math/0510106

40.  Hilbert schemes of points on the minimal resolution and soliton equations, (with Z. Qin), Contemp. Math.  442 (2007), 435-462

     arXiv:math/0404540

2005

39.  Hilbert scheme intersection numbers, Hurwitz numbers, and Gromov-Witten invariants, (with W.-P. Li and Z. Qin), Contemp. Math. 392 (2005), 67-81.

38.  Integral operators and integral cohomology classes of Hilbert schemes, (with Z. Qin), Math. Ann. 331 (2005), 669-692

     arXiv:math/0405600 

2004

37.  The cohomology rings of Hilbert schemes via Jack polynomials, (with W.-P. Li and Z. Qin), CRM Proc. and Lect. Notes 38 (2004), 249-258

     arXiv:math/0411255

36.  Hilbert schemes, integrable hierarchies, and Gromov-Witten theory, (with W.-P. Li and Z. Qin), IMRN 40 (2004), 2085-2104

     arXiv:math/0302211

35.  The Bloch-Okounkov correlation functions at higher levels, (with Shun-Jen Cheng), Transformation Groups 9 (2004), no. 2, 133-142

     arXiv:math/0309186

34.  Correlation functions of strict partitions and twisted Fock spaces, Transformation Groups  9 (2004),  89-101

     arXiv:math/0303259

33.  Ideals of the cohomology rings of Hilbert schemes and their applications, (with W.-P. Li and Z. Qin), Trans. AMS 356 (2004), 245-265

     arXiv:math/0208070

32.  The Farahat-Higman ring of wreath products and Hilbert schemes, Adv. in Math. 187 (2004), 417-446

     arXiv:math/0205071

31.  Vertex algebras and the class algebras of wreath products, Proc. Lond. Math. Soc. 88 (2004), 381-404 

     arXiv:math/0203004

2003

30.  Universal rings arising in geometry and group theory, In: S. Cutkosky et al (eds.), Vector bundles and representation theory, Contemp. Math. 322 (2003), 125-140

     arXiv:math/0211093

29.  Stability of the cohomology rings of Hilbert schemes of points on surfaces, (with W.-P. Li and Z. Qin), J. reine angew. Math.  554 (2003), 217-234

     arXiv:math/0107139

28.  Lie subalgebras of differential operators on the super circle, (with S.-J. Cheng), Publ. RIMS  39 (2003), 545-600

     arXiv:math/0103092

27.  Equivariant K-theory, generalized symmetric products, and twisted Heisenberg algebra, Commun. Math. Phys.  234 (2003), 101-127

     arXiv:math/0104168

2002

26.  Hilbert schemes and symmetric products: a dictionary, (with Zhenbo Qin), Contemp. Math. 310 (2002), 233-257

     arXiv:math/0112070

25.  Hilbert schemes and W algebras, (withW.-P. Li and Z. Qin), Internat. Math. Res. Notices 27 (2002), 1427-1456

           arXiv:math/0111047

24.  Algebraic structures behind Hilbert schemes and wreath products, Contemp. Math. 297 (2002), 271-295

     arXiv:math/0011103

23.  Vertex algebras and the cohomology ring structure of Hilbert schemes of points on surfaces, (with W.-P. Li and Z. Qin), Math. Ann. 324 (2002), 105-133

     arXiv:math/0009132

22.  Twisted vertex representations and spin characters, (with N. Jing), Math. Z. 239 (2002), 715-746

     arXiv:math/0104127

21.  Twisted vertex representations via spin groups and the McKay correspondence, (with I. Frenkel and N. Jing), Duke Math. J.  111 (2002), 51-96

      arXiv:math/0007159 

2001

        20.  Generators for the cohomology ring of Hilbert schemes of points on surfaces, (with W.-P. Li and Z. Qin), IMRN 20 (2001), 1057-1074

               arXiv:math/0009167

        19.  Virasoro algebra and wreath product convolution, (with I. Frenkel), J. Algebra 242 (2001), 656-671

               arXiv:math/0006087

        18.  Orbifold Hodge numbers of the wreath product orbifolds, (with J. Zhou), J. Geom. Phys. 38 (2001), 153-170

               arXiv:math/0005124   

        17.  Howe duality for Lie superalgbras, (with S.-J. Cheng), Compositio Math. 128 (2001), 55-94

               arXiv:math/0008093

        16.  Resolution of singularities of null cones, Canad. Math. Bull. 44 (2001), 491-503

               arXiv:math/0005078

        15.  Lagrangian construction of the (gl_n, gl_m)-duality, Commun. in Contemp. Math. 3 (2001), 201-214

     arXiv:math/9907154

2000

        14.  Remarks on Schur-Howe-Sergeev duality, (with S.-J. Cheng),  Lett. Math. Phys. 52 (2000), 143-153

           arXiv:math/0008109

        13.  Quantum vertex representations via finite groups and the McKay correspondence, (with I. Frenkel and N. Jing), Comm. Math. Phys.  211 (2000), 365-393

           arXiv:math/9907175

        12.  Vertex representations via finite groups and the McKay correspondence,  (with I. Frenkel and N. Jing), IMRN 4 (2000), 195-222

           arXiv:math/9907166

        11.  Equivariant K-theory, wreath products, and Heisenberg algebra, Duke Math. J.  103 (2000), 1-23

 arXiv:math/9907151 

1999

      10.  Dimension of a minimal nilpotent orbit, Proc. AMS. 127 (1999), 935-936

           arXiv:math/9907141    

        9. Dual pairs and infinite dimensional Lie algebras, Contemp. Math.   248 (1999), 453-469

          arXiv:math/9907140

        8.  Duality in infinite dimensional Fock representations, Commun. in Contemp. Math. 1 (1999), 155-199

           arXiv:q-alg/9710035

        7.  Dual pairs and tensor categories of modules over Lie algebras \widehat{gl}_{\infty} and W_{1+\infty}, J. Algebra 216 (1999), 159-177

           arXiv:q-alg/9709034

1998

        6.  Quasifinite representations of classical Lie subalgebras of  W_{1+\infty}, (with V. Kac and C.H. Yan), Adv. in Math. 139 (1998), 56-140 

           arXiv:math/9801136 

        5.  Classification of irreducible modules of W_3 algebra with c = -2, Commun. Math. Phys.  195 (1998), 113-128  

           arXiv:q-alg/9708016

        4. W_{1 +\infty} algebra,  W_3 algebra, and Friedan-Martinec-Shenker bosonization, Commun. Math. Phys.  195 (1998), 95-111

  arXiv:q-alg/9708008

1995

        3.  W_{1+\infty} and W(gl_N) with central charge N, (with E. Frenkel, V. Kac and A. Radul), Commun. Math. Phys. 170 (1995), 337-357

  arXiv:hep-th/9405121 

1994

        2.  Vertex operator superalgebras and their representations, (with V. Kac), Contemp. Math. 175 (1994), 161-191

  arXiv:hep-th/9312065

1993

        1.  Rationality of Virasoro vertex operator algebras, IMRN 7 (1993), 197--211