Equivariant $\mathcal{D}$-modules on rigid analytic spaces

TL;DR

This paper introduces coadmissible equivariant -modules on smooth rigid analytic spaces and connects them to admissible locally analytic representations of semisimple p-adic Lie groups, advancing the understanding of p-adic representation theory.

Contribution

It defines a new class of -modules on rigid spaces and establishes their relationship with locally analytic representations of p-adic groups.

Findings

Established a correspondence between -modules and p-adic group representations

Defined coadmissible equivariant -modules on rigid analytic spaces

Linked geometric objects to representation theory in p-adic context

Abstract

We define coadmissible equivariant $\mathcal{D}$-modules on smooth rigid analytic spaces and relate them to admissible locally analytic representations of semisimple $p$-adic Lie groups.