Quantum group of type A and representations of queer Lie superalgebra

Chih Whi Chen, Shun Jen Cheng

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We establish a maximal parabolic version of the Kazhdan–Lusztig conjecture [10, Conjecture 5.10] for the BGG category Ok,ζ of q(n)-modules of “±ζ-weights”, where k≤n and ζ∈C∖Z. As a consequence, the irreducible characters of these q(n)-modules in this maximal parabolic category are given by the Kazhdan–Lusztig polynomials of type A Lie algebras. As an application, closed character formulas for a class of q(n)-modules resembling polynomial and Kostant modules of the general linear Lie superalgebras are obtained.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalJournal of Algebra
Volume473
DOIs
StatePublished - 1 Mar 2017

Keywords

  • BGG category
  • Brundan–Kazhdan–Lusztig conjecture
  • Canonical basis
  • Dual canonical basis
  • Irreducible character
  • Kac–Wakimoto character formula
  • Maximal parabolic subcategory
  • Quantum group
  • Queer Lie superalgebra
  • Sergeev–Pragacz character formula

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