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Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Tableau Formulas for One-Row Macdonald Polynomials of Types Cn and Dn
Інший ID:
2010 Mathematics Subject Classification: 33D52; 33D80
DOI:10.3842/SIGMA.2015.100
DOI:10.3842/SIGMA.2015.100
Посилання:
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.
Підтримка:
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].
Дата:
2015
Переглядів:
759
Завантажень:
293
Анотація:
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.
