Kazhdan-Lusztig theory of super type D and quantum symmetric pairs

Author:

Bao Huanchen

Abstract

We reformulate the Kazhdan-Lusztig theory for the BGG category O \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 O \mathcal {O} of the ortho-symplectic Lie superalgebra o s p ( 2 m | 2 n ) \mathfrak {osp}(2m|2n) .

Publisher

American Mathematical Society (AMS)

Subject

Mathematics (miscellaneous)

Reference22 articles.

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4. [BK15] M. Balagovic and S. Kolb Universal K-matrix for quantum symmetric pairs, arXiv:1507.06276.

5. [Br1] J. Brundan, Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra 𝔤𝔩(𝔪|𝔫), J. Amer. Math. Soc. 16 (2003), 185–231.

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