Non-Stationary Ruijsenaars Functions for κ = t⁻¹ᐟᴺ and Intertwining Operators of Ding-Iohara-Miki Algebra
We construct the non-stationary Ruijsenaars functions (affine analogue of the Macdonald functions) in the special case κ=t⁻¹ᐟᴺ, using the intertwining operators of the Ding-Iohara-Miki algebra (DIM algebra) associated with -fold Fock tensor spaces. By the -duality of the intertwiners, another expres...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
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Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211004 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Non-Stationary Ruijsenaars Functions for κ = t⁻¹ᐟᴺ and Intertwining Operators of Ding-Iohara-Miki Algebra. Masayuki Fukuda, Yusuke Ohkubo and Jun'ichi Shiraishi. SIGMA 16 (2020), 116, 55 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862731473997529088 |
|---|---|
| author | Fukuda, Masayuki Ohkubo, Yusuke Shiraishi, Jun'ichi |
| author_facet | Fukuda, Masayuki Ohkubo, Yusuke Shiraishi, Jun'ichi |
| citation_txt | Non-Stationary Ruijsenaars Functions for κ = t⁻¹ᐟᴺ and Intertwining Operators of Ding-Iohara-Miki Algebra. Masayuki Fukuda, Yusuke Ohkubo and Jun'ichi Shiraishi. SIGMA 16 (2020), 116, 55 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We construct the non-stationary Ruijsenaars functions (affine analogue of the Macdonald functions) in the special case κ=t⁻¹ᐟᴺ, using the intertwining operators of the Ding-Iohara-Miki algebra (DIM algebra) associated with -fold Fock tensor spaces. By the -duality of the intertwiners, another expression is obtained for the non-stationary Ruijsenaars functions with κ = t⁻¹ᐟᴺ, which can be regarded as a natural elliptic lift of the asymptotic Macdonald functions to the multivariate elliptic hypergeometric series. We also investigate some properties of the vertex operator of the DIM algebra appearing in the present algebraic framework: an integral operator which commutes with the elliptic Ruijsenaars operator, and the degeneration of the vertex operators to the Virasoro primary fields in the conformal limit → 1.
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| first_indexed | 2026-04-17T15:19:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211004 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T15:19:25Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fukuda, Masayuki Ohkubo, Yusuke Shiraishi, Jun'ichi 2025-12-22T09:23:57Z 2020 Non-Stationary Ruijsenaars Functions for κ = t⁻¹ᐟᴺ and Intertwining Operators of Ding-Iohara-Miki Algebra. Masayuki Fukuda, Yusuke Ohkubo and Jun'ichi Shiraishi. SIGMA 16 (2020), 116, 55 pages 1815-0659 2020 Mathematics Subject Classification: 33D52; 81R10 arXiv:2002.00243 https://nasplib.isofts.kiev.ua/handle/123456789/211004 https://doi.org/10.3842/SIGMA.2020.116 We construct the non-stationary Ruijsenaars functions (affine analogue of the Macdonald functions) in the special case κ=t⁻¹ᐟᴺ, using the intertwining operators of the Ding-Iohara-Miki algebra (DIM algebra) associated with -fold Fock tensor spaces. By the -duality of the intertwiners, another expression is obtained for the non-stationary Ruijsenaars functions with κ = t⁻¹ᐟᴺ, which can be regarded as a natural elliptic lift of the asymptotic Macdonald functions to the multivariate elliptic hypergeometric series. We also investigate some properties of the vertex operator of the DIM algebra appearing in the present algebraic framework: an integral operator which commutes with the elliptic Ruijsenaars operator, and the degeneration of the vertex operators to the Virasoro primary fields in the conformal limit → 1. The authors would like to thank H. Awata, B. Feigin, A. Hoshino, H. Kanno, Y. Matsuo, M. Noumi, and S. Yanagida for valuable comments. The authors are also grateful to the referees for helpful feedback. Their search for J.S. is supported by JSPS KAKENHI (Grant Numbers 19K03512). Y.O. and M.F. are partially supported by Grant-in-Aid for JSPS Research Fellow (Y.O.: 18J00754, M.F.: 17J02745). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Non-Stationary Ruijsenaars Functions for κ = t⁻¹ᐟᴺ and Intertwining Operators of Ding-Iohara-Miki Algebra Article published earlier |
| spellingShingle | Non-Stationary Ruijsenaars Functions for κ = t⁻¹ᐟᴺ and Intertwining Operators of Ding-Iohara-Miki Algebra Fukuda, Masayuki Ohkubo, Yusuke Shiraishi, Jun'ichi |
| title | Non-Stationary Ruijsenaars Functions for κ = t⁻¹ᐟᴺ and Intertwining Operators of Ding-Iohara-Miki Algebra |
| title_full | Non-Stationary Ruijsenaars Functions for κ = t⁻¹ᐟᴺ and Intertwining Operators of Ding-Iohara-Miki Algebra |
| title_fullStr | Non-Stationary Ruijsenaars Functions for κ = t⁻¹ᐟᴺ and Intertwining Operators of Ding-Iohara-Miki Algebra |
| title_full_unstemmed | Non-Stationary Ruijsenaars Functions for κ = t⁻¹ᐟᴺ and Intertwining Operators of Ding-Iohara-Miki Algebra |
| title_short | Non-Stationary Ruijsenaars Functions for κ = t⁻¹ᐟᴺ and Intertwining Operators of Ding-Iohara-Miki Algebra |
| title_sort | non-stationary ruijsenaars functions for κ = t⁻¹ᐟᴺ and intertwining operators of ding-iohara-miki algebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211004 |
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