Gruson-Serganova character formulas and the Duflo-Serganova cohomology functor

Maria Gorelik, Thorsten Heidersdorf

Research output: Contribution to journalArticlepeer-review

Abstract

We establish an explicit formula for the character of an irreducible finite-dimensional representation of gl(m|n). The formula is a finite sum with integer coefficients in terms of a basis epsilon(mu) (Euler characters) of the character ring. We prove a simple formula for the behavior of the "superversion" of epsilon(mu) in the gl(m|n)and osp(m|2n)-case under the map ds on the supercharacter ring induced by the Duflo-Serganova cohomology functor DS. As an application, we get combinatorial formulas for superdimensions, dimensions and g(0)-decompositions for gl(m|n)and osp(m|2n).
Original languageEnglish
Pages (from-to)1-54
Number of pages54
JournalJournal fur die Reine und Angewandte Mathematik
Volume2023
Issue number798
Early online dateApr 2023
DOIs
StatePublished - 1 May 2023

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