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
Дата:2020
Автори: Fukuda, Masayuki, Ohkubo, Yusuke, Shiraishi, Jun'ichi
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2020
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
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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.
first_indexed 2026-04-17T15:19:25Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-04-17T15:19:25Z
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publisher Інститут математики НАН України
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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).
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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
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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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