Universal deformation rings of group representations, with an application of Brauer's generalized decomposition numbers

TL;DR

This paper introduces deformation theory for linear group representations, focusing on finite groups, and demonstrates how Brauer's generalized decomposition numbers can explicitly determine universal deformation rings.

Contribution

It applies Brauer's generalized decomposition numbers to compute universal deformation rings of finite group representations, extending deformation theory methods.

Findings

Explicit determination of universal deformation rings using Brauer's numbers

Application of deformation theory to finite groups

Enhanced understanding of representation deformations

Abstract

We give an introduction to the deformation theory of linear representations of profinite groups which Mazur initiated in the 1980's. We then consider the case of representations of finite groups. We show how Brauer's generalized decomposition numbers can be used in some cases to explicitly determine universal deformation rings.