On symmetries of the Duflo-Serganova functor

Alexander Sherman

On symmetries of the Duflo-Serganova functor

Representation Theory 2023-07-14 v2

Authors: Alexander Sherman

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 $P(n)$ .

Keywords

Duflo-Serganova functor Lie superalgebra Lie supergroup associative superalgebra Kac module GL(n|n) P(n)

Cite

@article{arxiv.2201.12808,
  title  = {On symmetries of the Duflo-Serganova functor},
  author = {Alexander Sherman},
  journal= {arXiv preprint arXiv:2201.12808},
  year   = {2023}
}

Comments

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

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