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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Kazhdan-Lusztig theory of super type D and quantum symmetric pairs
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Represent. Theory 21 (2017), 247-276 Request permission


We reformulate the Kazhdan-Lusztig theory for the BGG category $\mathcal {O}$ of Lie algebras of type D via the theory of canonical bases arising from quantum symmetric pairs initiated by Weiqiang Wang and the author. This is further applied to formulate and establish for the first time the Kazhdan-Lusztig theory for the BGG category $\mathcal {O}$ of the ortho-symplectic Lie superalgebra $\mathfrak {osp}(2m|2n)$.
  • H. Bao, J. Kujawa, Y. Li, and W. Wang, Geometric Schur duality of classical type, (with Appendix by Bao, Li and Wang), arXiv:1404.4000v3.
  • Alexandre Beĭlinson and Joseph Bernstein, Localisation de $g$-modules, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 1, 15–18 (French, with English summary). MR 610137
  • J.-L. Brylinski and M. Kashiwara, Kazhdan-Lusztig conjecture and holonomic systems, Invent. Math. 64 (1981), no. 3, 387–410. MR 632980, DOI 10.1007/BF01389272
  • M. Balagovic and S. Kolb Universal K-matrix for quantum symmetric pairs, arXiv:1507.06276.
  • J. Brundan, Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra $\mathfrak {gl}(m|n)$, J. Amer. Math. Soc. 16 (2003), 185–231.
  • J. Brundan, I. Losev, and B. Webster, Tensor product categorifications and the super Kazhdan-Lusztig conjecture, preprint 2013, arXiv:1310.0349.
  • H. Bao and W. Wang, A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs, arXiv:1310.0103v2.
  • H. Bao and W. Wang, Canonical bases arising from quantum symmetric pairs, in preparation.
  • S.-J. Cheng, N. Lam, and W. Wang, Super duality and irreducible characters of ortho-symplectic Lie superalgebras, Invent. Math. 183 (2011), 189–224.
  • S.-J. Cheng, N. Lam, and W. Wang, Brundan-Kazhdan-Lusztig conjecture for general linear Lie superalgebras, Duke J. Math. (2015),
  • Shun-Jen Cheng and Weiqiang Wang, Dualities and representations of Lie superalgebras, Graduate Studies in Mathematics, vol. 144, American Mathematical Society, Providence, RI, 2012. MR 3012224, DOI 10.1090/gsm/144
  • M. Ehrig and C. Stroppel, Nazarov-Wenzl algebras, coideal subalgebras and categorified skew Howe Duality, arXiv:1310.1972.
  • Zhaobing Fan and Yiqiang Li, Geometric Schur duality of classical type, II, Trans. Amer. Math. Soc. Ser. B 2 (2015), 51–92. MR 3402700, DOI 10.1090/btran/8
  • Michio Jimbo, A $q$-analogue of $U({\mathfrak {g}}{\mathfrak {l}}(N+1))$, Hecke algebra, and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), no. 3, 247–252. MR 841713, DOI 10.1007/BF00400222
  • V. G. Kac, Lie superalgebras, Advances in Math. 26 (1977), no. 1, 8–96. MR 486011, DOI 10.1016/0001-8708(77)90017-2
  • M. Kashiwara, On crystal bases of the $Q$-analogue of universal enveloping algebras, Duke Math. J. 63 (1991), no. 2, 465–516. MR 1115118, DOI 10.1215/S0012-7094-91-06321-0
  • David Kazhdan and George Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), no. 2, 165–184. MR 560412, DOI 10.1007/BF01390031
  • Stefan Kolb, Quantum symmetric Kac-Moody pairs, Adv. Math. 267 (2014), 395–469. MR 3269184, DOI 10.1016/j.aim.2014.08.010
  • G. Letzter, Symmetric pairs for quantized enveloping algebras, J. Algebra 220, 729Ж767 (1999).
  • G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), 447–498.
  • G. Lusztig, Introduction to Quantum Groups, Modern Birkhäuser Classics, Reprint of the 1993 Edition, Birkhäuser, Boston, 2010.
  • Y. Li and W. Wang, Positivity vs negativity of canonical bases, arXiv:1501.00688v3.
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Additional Information
  • Huanchen Bao
  • Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
  • MR Author ID: 1193508
  • Email:
  • Received by editor(s): January 19, 2017
  • Received by editor(s) in revised form: July 25, 2017
  • Published electronically: September 13, 2017
  • © Copyright 2017 American Mathematical Society
  • Journal: Represent. Theory 21 (2017), 247-276
  • MSC (2010): Primary 17B10
  • DOI:
  • MathSciNet review: 3696376