Alexander Sherman
Published 2022-01-30Version 1
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 $P(n)$.
Comments: 23 pages; comments welcome!
The Duflo-Serganova functor and Grothendieck rings of Lie superalgebras
Generators and relations for Lie superalgebras of Cartan type
Vector fields on $\mathfrak{osp}_{2m|2n}(\mathbb C)$- and $π\mathfrak{sp}_{n}(\mathbb C)$-flag supermanifolds
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