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Combinatorial formula for Macdonald polynomials, Bethe Ansatz, and generic Macdonald polynomials

Andrei Okounkov
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Abstract

We give a direct proof of the combinatorial formula for interpolation Macdonald polynomials by introducing certain polynomials, which we call generic Macdonald polynomials, which depend on $d$ additional parameters and specialize to all Macdonald polynomials of degree $d$. The form of these generic polynomials is that of a Bethe eigenfunction and they imitate, on a more elementary level, the $R$-matrix construction of quantum immanants.

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BibTeXRIS

Andrei Okounkov. 2000-08-13. Combinatorial formula for Macdonald polynomials, Bethe Ansatz, and generic Macdonald polynomials. https://arxiv.org/abs/math/0008094

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