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<p>We initiate a study of the symmetries of the Duflo–Serganova functor, <i>DS</i>. 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 <i>DS</i>. In addition, we connect our work to a computation of Heidersdorf and Weissauer which computed <i>DS</i><sub><i>x</i></sub> for a maximal rank <i>x</i> on Kac-modules for GL(<i>n</i>∣<i>n</i>), and extend the ideas and results to <i>P</i>(<i>n</i>).</p>

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On symmetries of the Duflo–Serganova functor

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  • 发表日期：

    2025年3月27日

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  • Alexander Sherman

摘要

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).