Functor morphing and representations of automorphism groups of modules

TL;DR

This paper presents a new approach to understanding irreducible representations of automorphism groups of finite modules over local rings by using stratification and invariant theory within symmetric monoidal categories.

Contribution

It introduces a novel strategy to decompose and analyze irreducible representations of automorphism groups via a hierarchical framework and categorical methods.

Findings

Automorphism groups fit into a hierarchical structure.

Irreducible representations can be stratified into smaller components.

The approach leverages symmetric monoidal categories and invariant theory.

Abstract

We introduce a strategy to study irreducible representations of automorphism groups of finite modules over local rings. We prove that these automorphism groups fit in a hierarchy that facilitates a stratification of their irreducible representations in terms of smaller building blocks using symmetric monoidal categories and invariant theory.