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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.16143 |
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Table of Contents:
- 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 $\widetilde{\mathbb{G}_x}$ of this functor, recently introduced by A.Sherman, for a wide class of supergroups $\mathbb{G}$, and apply it to the case when $\mathbb{G}$ is $\mathrm{GL}(m|n)$ or $\mathrm{Q}(n)$, and a square zero odd element $x\in \mathrm{Lie}(\mathbb{G})$ has minimal or maximal rank. For any quasi-reductive supergroup $\mathbb{G}$, which has a pair of specific parabolic supersubgroups, we prove a criterion of injectivity of a $\mathbb{G}$-supermodule, involving vanishing of Duflo-Serganova functor on it.