Generalized Gelfand-Cetlin data and abelianization

Abstract

This manuscript aims to advance existing approaches to the abelianization of symplectic quotients. Two such approaches include the imploded cross-sections of Guillemin-Jeffrey-Sjamaar, and the Gelfand-Cetlin abelianizations of the first author and Weitsman. Using our notion of generalized Gelfand-Cetlin data, we generalize the second approach to account for irregular values of the moment map. Connections to symplectic implosion are emphasized throughout this manuscript.