Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn
We present explicit formulas for the Macdonald polynomials of types Cn and Dn in the one-row case. In view of the combinatorial structure, we call them ''tableau formulas''. For the construction of the tableau formulas, we apply some transformation formulas for the basic hypergeo...
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| Дата: | 2015 |
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| Автори: | , , , , |
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Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147163 |
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| Цитувати: | Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn / B. Feigin, A. Hoshino, M. Noumi, J. Shibahara, J. Shiraishi // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 14 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1471632025-02-09T12:47:57Z Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn Feigin, B. Hoshino, A. Noumi, M. Shibahara, J. Shiraishi, J. We present explicit formulas for the Macdonald polynomials of types Cn and Dn in the one-row case. In view of the combinatorial structure, we call them ''tableau formulas''. For the construction of the tableau formulas, we apply some transformation formulas for the basic hypergeometric series involving very well-poised balanced ₁₂W₁₁ series. We remark that the correlation functions of the deformed W algebra generators automatically give rise to the tableau formulas when we principally specialize the coordinate variables. This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications. The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html. This study was carried out within The National Research University Higher School of Economics Academic Fund Program in 2013–2014, research grant No.12-01-0016k. Research of J.S. is supported by the Grant-in-Aid for Scientific Research C-24540206. The financial support from the Government of the Russian Federation within the framework of the implementation of the 5-100 Programme Roadmap of the National Research University Higher School of Economics is acknowledged. The authors sincerely thank the anonymous referees for valuable comments and informing them of the connection between one of our results (Theorem 2.2) and the known fact obtained in [7]. 2015 Article Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn / B. Feigin, A. Hoshino, M. Noumi, J. Shibahara, J. Shiraishi // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 14 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D52; 33D80 DOI:10.3842/SIGMA.2015.100 https://nasplib.isofts.kiev.ua/handle/123456789/147163 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We present explicit formulas for the Macdonald polynomials of types Cn and Dn in the one-row case. In view of the combinatorial structure, we call them ''tableau formulas''. For the construction of the tableau formulas, we apply some transformation formulas for the basic hypergeometric series involving very well-poised balanced ₁₂W₁₁ series. We remark that the correlation functions of the deformed W algebra generators automatically give rise to the tableau formulas when we principally specialize the coordinate variables. |
| format |
Article |
| author |
Feigin, B. Hoshino, A. Noumi, M. Shibahara, J. Shiraishi, J. |
| spellingShingle |
Feigin, B. Hoshino, A. Noumi, M. Shibahara, J. Shiraishi, J. Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Feigin, B. Hoshino, A. Noumi, M. Shibahara, J. Shiraishi, J. |
| author_sort |
Feigin, B. |
| title |
Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn |
| title_short |
Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn |
| title_full |
Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn |
| title_fullStr |
Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn |
| title_full_unstemmed |
Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn |
| title_sort |
tableau formulas for one-row macdonald polynomials of types cn and dn |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147163 |
| citation_txt |
Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn / B. Feigin, A. Hoshino, M. Noumi, J. Shibahara, J. Shiraishi // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 14 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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