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- W4320231963 abstract "We study various categories of Whittaker modules over a type I Lie superalgebra realized as cokernel categories that fit into the framework of properly stratified categories. These categories are the target of the Backelin functor $Gamma_zeta$. We show that these categories can be described, up to equivalence, as Serre quotients of the BGG category $mathcal O$ and of certain singular categories of Harish-Chandra $(mathfrak g,mathfrak g_{bar 0})$-bimodules. We also show that $Gamma_zeta$ is a realization of the Serre quotient functor. We further investigate a $q$-symmetrized Fock space over a quantum group of type A and prove that, for general linear Lie superalgebras our Whittaker categories, the functor $Gamma_zeta$ and various realizations of Serre quotients and Serre quotient functors categorify this $q$-symmetrized Fock space and its $q$-symmetrizer. In this picture, the canonical and dual canonical bases in this $q$-symmetrized Fock space correspond to tilting and simple objects in these Whittaker categories, respectively." @default.
- W4320231963 created "2023-02-13" @default.
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- W4320231963 creator A5043623116 @default.
- W4320231963 date "2022-03-01" @default.
- W4320231963 modified "2023-09-23" @default.
- W4320231963 title "Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras" @default.
- W4320231963 doi "https://doi.org/10.48550/arxiv.2203.00541" @default.
- W4320231963 hasPublicationYear "2022" @default.
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