Geodesic
Tableau Formulas for One-Row Macdonald Polynomials of Types $C_n$ and $D_n$
Symmetry, integrability and geometry: methods and applications, Tome 11 (2015) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{SIGMA_2015_11_a99,
     author = {Boris Feigin and Ayumu Hoshino and Masatoshi Noumi and Jun Shibahara and Jun'ichi Shiraishi},
     title = {Tableau {Formulas} for {One-Row} {Macdonald} {Polynomials} of {Types} $C_n$ and $D_n$},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2015},
     volume = {11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a99/}
}
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Boris Feigin; Ayumu Hoshino; Masatoshi Noumi; Jun Shibahara; Jun'ichi Shiraishi. Tableau Formulas for One-Row Macdonald Polynomials of Types $C_n$ and $D_n$. Symmetry, integrability and geometry: methods and applications, Tome 11 (2015). http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a99/

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