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

2021/04/26 by Gorelik, Maria, Heidersdorf, Thorsten · 3 citations
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2104.12634

Abstract

We establish an explicit formula for the character of an irreducible finite-dimensional representation of \mathfrakgl(m|n). The formula is a finite sum with integer coefficients in terms of a basis E_μ (Euler characters) of the character ring. We prove a simple formula for the behaviour of the ``superversion'' of E_μ in the \mathfrakgl(m|n) and \mathfrakosp(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 \mathfrakg₀-decompositions for \mathfrakgl(m|n) and \mathfrakosp(m|2n).

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