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

Bao, Huanchen

doi:10.1090/ert/505

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

Represent. Theory 21 (2017), 247-276

DOI: https://doi.org/10.1090/ert/505

Published electronically: September 13, 2017

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Abstract:

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 $\mathfrak {osp}(2m|2n)$.

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