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Quasi-parabolic Kazhdan-Lusztig bases and reflection subgroups (2305.12290v2)
Published 20 May 2023 in math.RT
Abstract: Recently, Wang and the second author constructed a bar involution and canonical basis for a quasi-permutation module of the Hecke algebra associated to a type B Weyl group $W$, where the basis is parameterized by left cosets of a quasi-parabolic reflection subgroup in $W$. In this paper we provide an alternative approach to these constructions, and then generalize to Coxeter groups which contain a product of type B Weyl groups as a parabolic subgroup.