On Solutions of the Fuji-Suzuki-Tsuda System
We derive the Fredholm determinant and series representation of the tau function of the Fuji-Suzuki-Tsuda system and its multivariate extension, thereby generalizing to higher rank the results obtained for Painlevé VI and the Garnier system. A special case of our construction gives a higher rank ana...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209881 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On Solutions of the Fuji-Suzuki-Tsuda System / P. Gavrylenko, N. Iorgov, O. Lisovyy // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 33 назв. — англ. |
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Gavrylenko, P. Iorgov, N. Lisovyy, O. 2025-11-28T09:41:21Z 2018 On Solutions of the Fuji-Suzuki-Tsuda System / P. Gavrylenko, N. Iorgov, O. Lisovyy // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 33 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33E17; 34M55; 34M56 arXiv: 1806.08650 https://nasplib.isofts.kiev.ua/handle/123456789/209881 https://doi.org/10.3842/SIGMA.2018.123 We derive the Fredholm determinant and series representation of the tau function of the Fuji-Suzuki-Tsuda system and its multivariate extension, thereby generalizing to higher rank the results obtained for Painlevé VI and the Garnier system. A special case of our construction gives a higher rank analog of the continuous hypergeometric kernel of Borodin and Olshanski. We also initiate the study of the algebraic braid group dynamics of semi-degenerate monodromy and, as a byproduct, obtain a direct isomonodromic proof of the AGT-W relation for c = N−1. The work of P.G. was partially supported by the Russian Academic Excellence Project ‘5-100’ and by the RSF grant No. 16-11-10160. In particular, the results of Section 6 were obtained using the support of the Russian Science Foundation. P.G. is a Young Russian Mathematics award winner and would like to thank their sponsors and jury. N.I. was partially supported by the National Academy of Sciences of Ukraine (project No. 0117U000238), by the Program of Fundamental Research of the Department of Physics and Astronomy of the NAS of Ukraine (project No. 0117U000240), and by the ICTP-SEENET-MTP project NT-03: Cosmology - Classical and Quantum Challenges. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Solutions of the Fuji-Suzuki-Tsuda System Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On Solutions of the Fuji-Suzuki-Tsuda System |
| spellingShingle |
On Solutions of the Fuji-Suzuki-Tsuda System Gavrylenko, P. Iorgov, N. Lisovyy, O. |
| title_short |
On Solutions of the Fuji-Suzuki-Tsuda System |
| title_full |
On Solutions of the Fuji-Suzuki-Tsuda System |
| title_fullStr |
On Solutions of the Fuji-Suzuki-Tsuda System |
| title_full_unstemmed |
On Solutions of the Fuji-Suzuki-Tsuda System |
| title_sort |
on solutions of the fuji-suzuki-tsuda system |
| author |
Gavrylenko, P. Iorgov, N. Lisovyy, O. |
| author_facet |
Gavrylenko, P. Iorgov, N. Lisovyy, O. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We derive the Fredholm determinant and series representation of the tau function of the Fuji-Suzuki-Tsuda system and its multivariate extension, thereby generalizing to higher rank the results obtained for Painlevé VI and the Garnier system. A special case of our construction gives a higher rank analog of the continuous hypergeometric kernel of Borodin and Olshanski. We also initiate the study of the algebraic braid group dynamics of semi-degenerate monodromy and, as a byproduct, obtain a direct isomonodromic proof of the AGT-W relation for c = N−1.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209881 |
| citation_txt |
On Solutions of the Fuji-Suzuki-Tsuda System / P. Gavrylenko, N. Iorgov, O. Lisovyy // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 33 назв. — англ. |
| work_keys_str_mv |
AT gavrylenkop onsolutionsofthefujisuzukitsudasystem AT iorgovn onsolutionsofthefujisuzukitsudasystem AT lisovyyo onsolutionsofthefujisuzukitsudasystem |
| first_indexed |
2025-12-07T16:53:21Z |
| last_indexed |
2025-12-07T16:53:21Z |
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1850886113003044864 |