On symmetries of the Duflo-Serganova functor

TL;DR

This paper explores symmetries of the Duflo-Serganova functor, introducing new algebraic constructions and extending previous computations from $GL(n|n)$ to $P(n)$, enhancing understanding of superalgebra actions.

Contribution

It provides new constructions of superalgebras acting on the Duflo-Serganova functor and extends symmetry results to the superalgebra $P(n)$.

Findings

New superalgebra constructions acting on the Duflo-Serganova functor

Extension of symmetry results from $GL(n|n)$ to $P(n)$

Connections to prior computations of $DS_x$ for maximal rank $x$

Abstract

We discuss several points regarding symmetries of the Duflo-Serganova functor. In particular we give new constructions of Lie superalgebras, Lie supergroups, and associative superalgebras which act on the Duflo-Serganova functor. We connect our work to a computation of Heidersdorf and Weissauer which computed $DS_x$ for a maximal rank $x$ on Kac-modules for $GL(n|n)$, and extend the ideas and results to $P(n)$.