Induction equivalence for equivariant D-modules on rigid analytic spaces

TL;DR

This paper establishes fundamental equivalences for equivariant D-modules on rigid analytic spaces, enabling classification and new representation constructions for p-adic Lie groups.

Contribution

It proves induction and Kashiwara equivalences for coadmissible equivariant D-modules, advancing the understanding of their structure and applications.

Findings

Classified equivariant D-modules supported on single orbits.

Constructed new irreducible locally analytic representations.

Extended Beilinson-Bernstein equivalence to p-adic groups.

Abstract

We prove an Induction Equivalence and a Kashiwara Equivalence for coadmissible equivariant D-modules on rigid analytic spaces. This allows us to completely classify such objects with support in a single orbit of a classical point with co-compact stabiliser. As an application, we use the locally analytic Beilinson-Bernstein equivalence to construct new examples of large families of topologically irreducible locally analytic representations of certain compact semisimple p-adic Lie groups.