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


Author: Huanchen Bao
Journal: Represent. Theory 21 (2017), 247-276
MSC (2010): Primary 17B10
DOI: https://doi.org/10.1090/ert/505
Published electronically: September 13, 2017
MathSciNet review: 3696376
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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\vert 2n)$.


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Additional Information

Huanchen Bao
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: huanchen@math.umd.edu

DOI: https://doi.org/10.1090/ert/505
Received by editor(s): January 19, 2017
Received by editor(s) in revised form: July 25, 2017
Published electronically: September 13, 2017
Article copyright: © Copyright 2017 American Mathematical Society