Induction equivalence for equivariant 𝒟-modules on rigid analytic spaces

Ardakov, Konstantin

doi:10.1090/ert/642

Induction equivalence for equivariant $\mathcal {D}$-modules on rigid analytic spaces
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by Konstantin Ardakov;

Represent. Theory 27 (2023), 177-247

DOI: https://doi.org/10.1090/ert/642

Published electronically: May 17, 2023

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Abstract:

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

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