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

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arxiv 1412.8001 v3 pith:KFZQ3LFQ submitted 2014-12-26 math.CO

Boris Feigin , Ayumu Hoshino , Masatoshi Noumi , Jun Shibahara , Jun'ichi Shiraishi This is my paper · ORCID
classification math.CO
keywords formulastableaumacdonaldone-rowpolynomialsseriestypesalgebra
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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.

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  1. Vogel's universality and Macdonald dimensions

    hep-th 2025-07 conditional novelty 4.0 of 10

    The paper gives a single rational formula for adjoint Macdonald dimensions that unifies the simply laced Lie algebras A_n, D_n, E6, E7, E8, plus explicit mixed-root-system dimension formulas.

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