On symmetries of the Duflo-Serganova functor

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 $D{S}_x$ for a maximal rank $x$ on Kac-modules for $GL(n|n)$, and extend the ideas and results to $P(n)$.

arXiv comment27 pages; added further explanations to certain sections; expanded introduction with more motivation; accepted for publication to Israel Journal of Mathematics; comments welcome!