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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2019 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2019
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210298 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862738970329219072 |
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| author | Loizides, Yi. |
| author_facet | Loizides, Yi. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T21:25:04Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210298 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:25:04Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | Quasi-Polynomials and the Singular [Q,R] = 0 Theorem Loizides, Yi. |
| title | 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_short | Quasi-Polynomials and the Singular [Q,R] = 0 Theorem |
| title_sort | quasi-polynomials and the singular [q,r] = 0 theorem |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210298 |
| work_keys_str_mv | AT loizidesyi quasipolynomialsandthesingularqr0theorem |