Abelianization and the Duistermaat–Heckman theorem

Abstract

We use the abelianization theorem of Crooks and Weitsman (2022) to prove a non‐abelian generalization of the Duistermaat–Heckman theorem for measures. Our main technical tools include the Gelfand–Cetlin data of Crooks and Weitsman (2022), examples of which are the Gelfand–Cetlin systems of Guillemin–Sternberg and generalizations thereof due to Hoffman–Lane.