Moment convexity of solvable locally compact groups

TL;DR

This paper introduces moment maps for continuous unitary representations of topological groups and proves convexity of their images for solvable locally compact groups, advancing understanding of their geometric structure.

Contribution

It establishes the convexity of the moment map image for representations of solvable locally compact groups, a novel result in the field.

Findings

Convexity of the moment map image for solvable groups

Introduction of moment maps for topological group representations

Extension of convexity results to a broad class of groups

Abstract

We introduce moment maps for continuous unitary representations of general topological groups. For solvable separable locally compact groups, we prove that the closure of the image of the moment map of any representation is convex.