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- W3191158591 abstract "Expanding the classic works of Kazhdan-Lusztig and Deodhar, we establish bar involutions and canonical (i.e., quasi-parabolic KL) bases on quasi-permutation modules over the type B Hecke algebra, where the bases are parameterized by cosets of (possibly non-parabolic) reflection subgroups of the Weyl group of type B. We formulate an $imath$Schur duality between an $imath$quantum group of type AIII (allowing black nodes in its Satake diagram) and a Hecke algebra of type B acting on a tensor space, providing a common generalization of Jimbo-Schur duality and Bao-Wang's quasi-split $imath$Schur duality. The quasi-parabolic KL bases on quasi-permutation Hecke modules are shown to match with the $imath$canonical basis on the tensor space. An inversion formula for quasi-parabolic KL polynomials is established via the $imath$Schur duality." @default.
- W3191158591 created "2021-08-16" @default.
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- W3191158591 date "2021-08-02" @default.
- W3191158591 modified "2023-09-24" @default.
- W3191158591 title "$imath$Schur duality and Kazhdan-Lusztig basis expanded" @default.
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- W3191158591 doi "https://doi.org/10.48550/arxiv.2108.00630" @default.
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