Whittaker Categories, Properly Stratified Categories and Fock Space Categorification for Lie Superalgebras

Chih Whi Chen, Shun Jen Cheng, Volodymyr Mazorchuk

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 Γ ζ. We show that these categories can be described, up to equivalence, as Serre quotients of the BGG category O and of certain singular categories of Harish-Chandra (g, g0 ¯) -bimodules. We also show that Γ ζ 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 Γ ζ 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.

Original languageEnglish
Pages (from-to)717-768
Number of pages52
JournalCommunications in Mathematical Physics
Volume401
Issue number1
DOIs
StatePublished - Jul 2023

Fingerprint

Dive into the research topics of 'Whittaker Categories, Properly Stratified Categories and Fock Space Categorification for Lie Superalgebras'. Together they form a unique fingerprint.

Cite this