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arXiv · 1612.05815

Grothendieck rings for Lie superalgebras and the Duflo-Serganova functor

Crystal Hoyt·Shifra Reif
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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 characters. 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.

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Crystal Hoyt, Shifra Reif. 2018-02-09. Grothendieck rings for Lie superalgebras and the Duflo-Serganova functor. https://doi.org/10.2140/ant.2018.12.2167

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