TY - JOUR

T1 - Whittaker Categories, Properly Stratified Categories and Fock Space Categorification for Lie Superalgebras

AU - Chen, Chih Whi

AU - Cheng, Shun Jen

AU - Mazorchuk, Volodymyr

N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2023/7

Y1 - 2023/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85147720142&partnerID=8YFLogxK

U2 - 10.1007/s00220-023-04652-6

DO - 10.1007/s00220-023-04652-6

M3 - 期刊論文

AN - SCOPUS:85147720142

SN - 0010-3616

VL - 401

SP - 717

EP - 768

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -