On symmetries of the Duflo–Serganova functor

Alexander Sherman

doi:10.1007/s11856-025-2745-y

On symmetries of the Duflo–Serganova functor

Alexander Sherman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We initiate a study of the symmetries of the Duflo–Serganova functor, DS. In particular we give new constructions of Lie superalgebras, Lie supergroups, and associative superalgebras which act on this functor. The main result is a realization that in the Kac–Moody setting, we find new odd infinitesimal symmetries of DS. In addition, 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).

Original language	English
Pages (from-to)	31-66
Number of pages	36
Journal	Israel Journal of Mathematics
Volume	269
Issue number	1
DOIs	https://doi.org/10.1007/s11856-025-2745-y
State	Published - 1 Oct 2025

ASJC Scopus subject areas

General Mathematics

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AB - We initiate a study of the symmetries of the Duflo–Serganova functor, DS. In particular we give new constructions of Lie superalgebras, Lie supergroups, and associative superalgebras which act on this functor. The main result is a realization that in the Kac–Moody setting, we find new odd infinitesimal symmetries of DS. In addition, we connect our work to a computation of Heidersdorf and Weissauer which computed DSx for a maximal rank x on Kac-modules for GL(n∣n), and extend the ideas and results to P(n).

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On symmetries of the Duflo–Serganova functor

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