Quasi-Polynomials and the Singular [Q,R] = 0 Theorem

In this short note, we revisit the 'shift-desingularization' version of the [Q, R] = 0 theorem for possibly singular symplectic quotients. We take as a starting point an elegant proof due to Szenes-Vergne of the quasi-polynomial behavior of the multiplicity as a function of the tensor powe...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2019
Main Author: Loizides, Yi.
Format: Article
Language:English
Published: Інститут математики НАН України 2019
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/210298
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Quasi-Polynomials and the Singular [Q,R] = 0 Theorem / Yi. Loizides // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 15 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-210298
record_format dspace
spelling Loizides, Yi.
2025-12-05T09:25:41Z
2019
Quasi-Polynomials and the Singular [Q,R] = 0 Theorem / Yi. Loizides // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 15 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 53D20; 53D50
arXiv: 1907.06113
https://nasplib.isofts.kiev.ua/handle/123456789/210298
https://doi.org/10.3842/SIGMA.2019.090
In this short note, we revisit the 'shift-desingularization' version of the [Q, R] = 0 theorem for possibly singular symplectic quotients. We take as a starting point an elegant proof due to Szenes-Vergne of the quasi-polynomial behavior of the multiplicity as a function of the tensor power of the prequantum line bundle. We use the Berline-Vergne index formula and the stationary phase expansion to compute the quasi-polynomial, adapting an early approach of Meinrenken.
I thank M. Vergne and E. Meinrenken for helpful conversations. I thank the referees for their helpful comments and suggestions that improved the article.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Quasi-Polynomials and the Singular [Q,R] = 0 Theorem
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Quasi-Polynomials and the Singular [Q,R] = 0 Theorem
spellingShingle Quasi-Polynomials and the Singular [Q,R] = 0 Theorem
Loizides, Yi.
title_short Quasi-Polynomials and the Singular [Q,R] = 0 Theorem
title_full Quasi-Polynomials and the Singular [Q,R] = 0 Theorem
title_fullStr Quasi-Polynomials and the Singular [Q,R] = 0 Theorem
title_full_unstemmed Quasi-Polynomials and the Singular [Q,R] = 0 Theorem
title_sort quasi-polynomials and the singular [q,r] = 0 theorem
author Loizides, Yi.
author_facet Loizides, Yi.
publishDate 2019
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description In this short note, we revisit the 'shift-desingularization' version of the [Q, R] = 0 theorem for possibly singular symplectic quotients. We take as a starting point an elegant proof due to Szenes-Vergne of the quasi-polynomial behavior of the multiplicity as a function of the tensor power of the prequantum line bundle. We use the Berline-Vergne index formula and the stationary phase expansion to compute the quasi-polynomial, adapting an early approach of Meinrenken.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/210298
citation_txt Quasi-Polynomials and the Singular [Q,R] = 0 Theorem / Yi. Loizides // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 15 назв. — англ.
work_keys_str_mv AT loizidesyi quasipolynomialsandthesingularqr0theorem
first_indexed 2025-12-07T21:25:04Z
last_indexed 2025-12-07T21:25:04Z
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