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arXiv · 2504.16699

Category O for p-adic rational Cherednik algebras

Fernando Peña Vázquez
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Abstract

We introduce the concept of a triangular decomposition for Banach and Fr\'echet-Stein algebras over $p$-adic fields, which allows us to define a category $\mathcal{O}$ for a wide array of topological algebras. In particular, we apply this concept to $p$-adic rational Cherednik algebras, which allows us to obtain an analytic version of the category $\mathcal{O}$ developed by Ginzburg, Guay, Opdam and Rouquier. Along the way, we study the global sections of $p$-adic Cherednik algebras on smooth Stein spaces, and determine their behavior with respect to the rigid analytic GAGA functor.

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Fernando Peña Vázquez. 2025-04-23. Category O for p-adic rational Cherednik algebras. https://arxiv.org/abs/2504.16699

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