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Abelianization and the Duistermaat–Heckman theorem

Abelianization and the Duistermaat-Heckman theorem
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 19 Jul 2023Embargo end date: 01 Jan 2023 English Publisher:WileyJournal:Bulletin of the London Mathematical Society, volume 55, pages 2,732-2,742 (issn: 0024-6093, eissn: 1469-2120, Copyright policy )
Authors: Peter Crooks; Jonathan Weitsman;

doi: 10.1112/blms.12891 , 10.48550/arxiv.2302.02421

arXiv: 2302.02421

Abelianization and the Duistermaat–Heckman theorem

Abstract

AbstractWe 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.

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Keywords

Duistermaat-Heckman measure, Symplectic manifolds (general theory), 53D20 (primary), 17B80 (secondary), Applications of Lie algebras and superalgebras to integrable systems, moment map, Mathematics - Symplectic Geometry, Momentum maps; symplectic reduction, FOS: Mathematics, Symplectic Geometry (math.SG), Radon-Nikodým, Kreĭn-Milman and related properties, Radon-Nikodym derivative

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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Average
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