Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation
We show the relation of the non-stationary difference equation proposed by one of the authors and the quantized discrete Painlevé VI equation. The five-dimensional Seiberg-Witten curve associated with the difference equation has a consistent four-dimensional limit. We also show that the original equ...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2023 |
| Main Authors: | , , , , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2023
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212042 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation. Hidetoshi Awata, Koji Hasegawa, Hiroaki Kanno, Ryo Ohkawa, Shamil Shakirov, Jun'ichi Shiraishi and Yasuhiko Yamada. SIGMA 19 (2023), 089, 47 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862735504586309632 |
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| author | Awata, Hidetoshi Hasegawa, Koji Kanno, Hiroaki Ohkawa, Ryo Shakirov, Shamil Shiraishi, Jun'ichi Yamada, Yasuhiko |
| author_facet | Awata, Hidetoshi Hasegawa, Koji Kanno, Hiroaki Ohkawa, Ryo Shakirov, Shamil Shiraishi, Jun'ichi Yamada, Yasuhiko |
| citation_txt | Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation. Hidetoshi Awata, Koji Hasegawa, Hiroaki Kanno, Ryo Ohkawa, Shamil Shakirov, Jun'ichi Shiraishi and Yasuhiko Yamada. SIGMA 19 (2023), 089, 47 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show the relation of the non-stationary difference equation proposed by one of the authors and the quantized discrete Painlevé VI equation. The five-dimensional Seiberg-Witten curve associated with the difference equation has a consistent four-dimensional limit. We also show that the original equation can be factorized as a coupled system for a pair of functions (⁽¹⁾, ⁽²⁾), which is a consequence of the identification of the Hamiltonian as a translation element in the extended affine Weyl group. We conjecture that the instanton partition function coming from the affine Laumon space provides a solution to the coupled system.
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| first_indexed | 2026-04-17T16:23:28Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212042 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T16:23:28Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Awata, Hidetoshi Hasegawa, Koji Kanno, Hiroaki Ohkawa, Ryo Shakirov, Shamil Shiraishi, Jun'ichi Yamada, Yasuhiko 2026-01-23T10:11:17Z 2023 Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation. Hidetoshi Awata, Koji Hasegawa, Hiroaki Kanno, Ryo Ohkawa, Shamil Shakirov, Jun'ichi Shiraishi and Yasuhiko Yamada. SIGMA 19 (2023), 089, 47 pages 1815-0659 2020 Mathematics Subject Classification: 14H70; 81R12; 81T40; 81T60 arXiv:2211.16772 https://nasplib.isofts.kiev.ua/handle/123456789/212042 https://doi.org/10.3842/SIGMA.2023.089 We show the relation of the non-stationary difference equation proposed by one of the authors and the quantized discrete Painlevé VI equation. The five-dimensional Seiberg-Witten curve associated with the difference equation has a consistent four-dimensional limit. We also show that the original equation can be factorized as a coupled system for a pair of functions (⁽¹⁾, ⁽²⁾), which is a consequence of the identification of the Hamiltonian as a translation element in the extended affine Weyl group. We conjecture that the instanton partition function coming from the affine Laumon space provides a solution to the coupled system. We would like to thank H. Hayashi, A.N. Kirillov, G. Kuroki, and H. Nakajima for useful discussions. We are also grateful to anonymous referees for useful comments and suggestions. Our work is supported in part by Grants-in-Aid for Scientific Research (Kakenhi): 18K03274 (H.K.), 21K03180 (R.O.), 19K03512 (J.S.), 19K03530 (J.S.), and 22H01116 (Y.Y.). The work of R.O. was partly supported by Osaka Central Advanced Mathematical Institute: MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics JPMXP0619217849, and the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation Article published earlier |
| spellingShingle | Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation Awata, Hidetoshi Hasegawa, Koji Kanno, Hiroaki Ohkawa, Ryo Shakirov, Shamil Shiraishi, Jun'ichi Yamada, Yasuhiko |
| title | Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation |
| title_full | Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation |
| title_fullStr | Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation |
| title_full_unstemmed | Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation |
| title_short | Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation |
| title_sort | non-stationary difference equation and affine laumon space: quantization of discrete painlevé equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212042 |
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