A few remarks 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 DS x for a maximal rank x on Kac-modules for GL(n|n), and extend the ideas and results to P (n).

On the Duflo-Serganova functor for the queer Lie superalgebra

“…Proof. By Lemma 3.1 of [29], DS x+y N ∼ = DS x+y N x 2 ,y 2 , so we may assume that x 2 = y 2 = 0. This reduces the statement to the case when g is (0|2)-dimensional commutative Lie superalgebra and N is a C-graded g module where x, y have different degrees.…”