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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.02786 |
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Table of Contents:
- The Steinberg tensor product theorem is a fundamental result in the modular representation theory of reductive algebraic groups. It describes any finite-dimensional simple module of highest weight $λ$ over such a group as the tensor product of Frobenius twists of simple modules with highest weights the weights appearing in a $p$-adic decomposition of $λ$, thereby reducing the character problem to a a finite collection of weights. In recent years this theorem has been extended to various quasi-reductive supergroup schemes. In this paper, we prove the analogous result for the general linear group scheme $GL(X)$ for any object $X$ in the Verlinde category $\mathrm{Ver}_p$.