Nonarchimedean coalgebras and coadmissible modules

TL;DR

This paper reformulates locally analytic representation theory using topological coalgebras and comodules, introducing admissible comodules that correspond to admissible representations of p-adic groups.

Contribution

It introduces the concept of admissible comodules in topological coalgebras, linking them to admissible representations in p-adic analysis.

Findings

Admissible comodules correspond to admissible representations.

Reformulation of representation theory in coalgebraic language.

Establishment of a new framework for locally analytic representations.

Abstract

We show that basic notions of locally analytic representation theory can be reformulated in the language of topological coalgebras (Hopf algebras) and comodules. We introduce the notion of admissible comodule and show that it corresponds to the notion of admissible representation in the case of topological Hopf algebra of locally analytic functions on a compact $p$-adic group.