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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
| Main Authors: | , , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147163 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862567692280528896 |
|---|---|
| author | Feigin, B. Hoshino, A. Noumi, M. Shibahara, J. Shiraishi, J. |
| author_facet | Feigin, B. Hoshino, A. Noumi, M. Shibahara, J. Shiraishi, J. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-26T00:12:34Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147163 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T00:12:34Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Feigin, B. Hoshino, A. Noumi, M. Shibahara, J. Shiraishi, J. 2019-02-13T17:59:37Z 2019-02-13T17:59:37Z 2015 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 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]. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn Article published earlier |
| spellingShingle | Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn Feigin, B. Hoshino, A. Noumi, M. Shibahara, J. Shiraishi, J. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147163 |
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