Generalized Gelfand-Cetlin data and abelianization

Peter Crooks; Mitchell Pound

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arXiv · 2610.05422

Generalized Gelfand-Cetlin data and abelianization

Peter Crooks·Mitchell Pound

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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.

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Peter Crooks, Mitchell Pound. 2026-10-04. Generalized Gelfand-Cetlin data and abelianization. https://arxiv.org/abs/2610.05422

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