On unitary deformations of smooth modular representations

TL;DR

This paper investigates how smooth modular representations of locally analytic groups can be lifted to unitary Banach space representations using deformation theory and Iwasawa modules.

Contribution

It introduces a novel approach combining deformation theory and Emerton's augmented Iwasawa modules to analyze liftings of modular representations.

Findings

Established criteria for lifting smooth modular representations to unitary Banach space representations.

Connected deformation theory with p-adic representation theory.

Provided new insights into the structure of locally analytic group representations.

Abstract

Let G be a locally analytic group. We use deformation theory and Emerton's 'augmented' Iwasawa modules to study the possible liftings of a given absolutely irreducible smooth modular representation of G to a unitary Banach space representation. Final version. Some minor items changed. Appears in Israel J. Math.