Duistermaat-Heckman distributions for group valued moment maps

TL;DR

This paper develops a new theoretical framework for equivariant Liouville forms and Duistermaat-Heckman distributions in the context of Hamiltonian group actions with group valued moment maps, with applications to moduli spaces of flat connections.

Contribution

It introduces a novel approach to group valued moment maps, extending classical symplectic geometry tools to new settings.

Findings

Established equivariant Liouville forms for group valued moment maps

Derived Duistermaat-Heckman distributions in this new context

Applied the theory to moduli spaces of flat connections

Abstract

We introduce equivariant Liouville forms and Duistermaat-Heckman distributions for Hamiltonian group actions with group valued moment maps. The theory is illustrated by applications to moduli spaces of flat connections on 2-manifolds.