Grothendieck rings for lie superalgebras and the Duflo–Serganova functor

Crystal Hoyt, Shifra Reif

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We show that the Duflo–Serganova functor on the category of finite-dimensional modules over a finite-dimensional contragredient Lie superalgebra induces a ring homomorphism on a natural quotient of the Grothendieck ring, which is isomorphic to the ring of supercharacters. We realize this homomorphism as a certain evaluation of functions related to the supersymmetry property. We use this realization to describe the kernel and image of the homomorphism induced by the Duflo–Serganova functor.

Original languageEnglish
Pages (from-to)2167-2184
Number of pages18
JournalAlgebra and Number Theory
Volume12
Issue number9
DOIs
StatePublished - 2018

Bibliographical note

Publisher Copyright:
© 2018, Mathematical Sciences Publishers. All rights reserved.

Keywords

  • Duflo-Serganova functor
  • Grothendieck ring
  • Lie superalgebra
  • Supercharacter
  • Supersymmetric Laurent polynomials

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