Irreducibility results for equivariant $\mathcal{D}$-modules on rigid analytic spaces

TL;DR

This paper establishes a broad irreducibility theorem for equivariant $$-modules on rigid analytic spaces and applies it to confirm the irreducibility of specific locally analytic representations.

Contribution

It provides a new general irreducibility result for equivariant $$-modules and offers a geometric proof for the irreducibility of certain locally analytic representations.

Findings

Proved a general irreducibility theorem for equivariant $$-modules.

Reproved the irreducibility of specific locally analytic representations.

Demonstrated the applicability of the theorem to geometric representation theory.

Abstract

We prove a general irreducibility result for geometrically induced coadmissible equivariant $\mathcal{D}$-modules on rigid analytic spaces. As an application, we geometrically reprove the irreducibility of certain locally analytic representations previously constructed by Orlik-Strauch.