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 |
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| Date: | 2019 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| 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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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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| 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 |
| _version_ |
1850886276852482048 |