Induction equivalence for equivariant 𝒟-modules on rigid analytic spaces

Abstract

We prove an Induction Equivalence and a Kashiwara Equivalence for coadmissible equivariant D \mathcal {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 p -adic Lie groups.