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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.
Related
- Abelianization of Symmetric Mapping Class Groups
- Abelianization and moment maps
- Representation and abelianization growth, particularly along expanding sequences
- Homogeneous symmetric trace-positive sextics with vanishing abelianization are sums of Hermitian squares and commutators
- Gelfand--Tsetlin bases for representations of Uq(gln) at roots of unity
BibTeX
@misc{crooks2026generalized,
title = {{Generalized Gelfand-Cetlin data and abelianization}},
author = {Peter Crooks and Mitchell Pound},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05422},
eprint = {2610.05422},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05422},
}
RIS
TY - UNPB
TI - Generalized Gelfand-Cetlin data and abelianization
AU - Peter Crooks
AU - Mitchell Pound
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05422
UR - https://arxiv.org/abs/2610.05422
AB - 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.
ER -