On induced locally analytic representations of locally analytic groups

TL;DR

This paper establishes conditions under which induced locally analytic representations of a subgroup are irreducible and introduces new locally analytic representations not obtainable through induction.

Contribution

It provides a criterion for irreducibility of induced representations and presents new examples of locally analytic representations outside this framework.

Findings

Induction criterion for irreducibility of locally analytic representations

New series of locally analytic representations not induced from subgroups

Extension of the Frommer-Orlik-Strauch theorem

Abstract

Let G be a locally analytic group and H < G - a locally analytic subgroup. The main result is the condition (similar to Frommer-Orlik-Strauch theorem) for induction of locally analytic H-representation to G to be irreducible. Also this paper contains a (new) series of locally analytic representations which do not arise in this way.