Notes on the Duflo-Serganova functor in positive characteristic

2025/03/20 by Alexandr N. Zubkov, Zubkov, A. N.
Mathematics · #14A22 14L15 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2503.16143

openalex publication_date 2025/03/20 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

We develop a fragment of the theory of Duflo-Serganova functor over a field of odd characteristic. We elaborate a method of computing the symmetry supergroup \widetilde\mathbbG_x of this functor, recently introduced by A.Sherman, for a wide class of supergroups \mathbbG, and apply it to the case when \mathbbG is GL(m|n) or Q(n), and a square zero odd element x∈ Lie(\mathbbG) has minimal or maximal rank. For any quasi-reductive supergroup \mathbbG, which has a pair of specific parabolic supersubgroups, we prove a criterion of injectivity of a \mathbbG-supermodule, involving vanishing of Duflo-Serganova functor on it.

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