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arXiv · 2411.10194

A remark on decomposing the canonical representation of the Drinfeld curve

Zhe Chen·Yushan Pan
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Abstract

Recently, by studying an explicit basis, K\"ock and Laurent give the decomposition of the $\overline{\mathbb{F}}_q[\mathrm{SL}_2(\mathbb{F}_q)]$-module of holomorphic forms on the Drinfeld curve. We present a crystalline cohomological proof of a weaker version of this result, without specifying a basis. As a by-product we observe a similar decomposition for the Gelfand--Graev representations.

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Zhe Chen, Yushan Pan. 2024-11-15. A remark on decomposing the canonical representation of the Drinfeld curve. https://arxiv.org/abs/2411.10194

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