Covariant representations of algebraic group actions and applications

TL;DR

This paper classifies irreducible covariant representations of algebraic affine group actions on affine varieties and explores applications to continuous representations of motion groups on Banach spaces.

Contribution

It adapts the Mackey machine to classify covariant representations in the algebraic setting and applies this to various examples.

Findings

Classification of irreducible covariant representations for algebraic affine groups

Extension of Mackey machine to algebraic group actions

Applications to continuous representations on Banach spaces

Abstract

If $G$ is an algebraic affine group acting on an affine variety $X$, there is a natural notion of covariant representation for the pair $(G,X)$. In this paper, we classify the irreducible covariant representations for any such pair by adapting the Mackey machine to this algebraic setting. Next, we give applications for continuous representations of motion groups on Banach spaces and other related examples.