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Symmetry, Integrability and Geometry: Methods and Applications, 2015, Volume 11, 100, 21 pp.
DOI: https://doi.org/10.3842/SIGMA.2015.100 (Mi sigma1081) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Tableau Formulas for One-Row Macdonald Polynomials of Types $C_n$ and $D_n$

Boris Feigina, Ayumu Hoshinob, Masatoshi Noumic, Jun Shibaharad, Jun'ichi Shiraishie

a National Research University Higher School of Economics, International Laboratory of Representation Theory and Mathematical Physics, Moscow, Russia
b Kagawa National College of Technology, 355 Chokushi-cho, Takamatsu, Kagawa 761-8058, Japan
c Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
d Hamamatsu University School of Medicine, 1-20-1 Handayama, Higashi-ku, Hamamatsu city, Shizuoka 431-3192, Japan
e Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914, Japan
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DOI: https://doi.org/10.3842/SIGMA.2015.100
Abstract: We present explicit formulas for the Macdonald polynomials of types $C_n$ and $D_n$ 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 ${}_{12}W_{11}$ series. We remark that the correlation functions of the deformed $\mathcal{W}$ algebra generators automatically give rise to the tableau formulas when we principally specialize the coordinate variables.
Keywords: Macdonald polynomials; deformed $\mathcal{W}$ algebras.
Received: May 19, 2015; in final form November 26, 2015; Published online December 5, 2015
Bibliographic databases:
Document Type: Article
MSC: 33D52; 33D80
Language: English
Citation: Boris Feigin, Ayumu Hoshino, Masatoshi Noumi, Jun Shibahara, Jun'ichi Shiraishi, “Tableau Formulas for One-Row Macdonald Polynomials of Types $C_n$ and $D_n$”, SIGMA, 11 (2015), 100, 21 pp.
Citation in format AMSBIB
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\by Boris~Feigin, Ayumu~Hoshino, Masatoshi~Noumi, Jun~Shibahara, Jun'ichi~Shiraishi
\paper Tableau Formulas for One-Row Macdonald Polynomials of Types $C_n$ and $D_n$
\jour SIGMA
\yr 2015
\vol 11
\papernumber 100
\totalpages 21
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