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(Shifted) Macdonald Polynomials: q-Integral Representation and Combinatorial Formula

Andrei Okounkov
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Abstract

We extend some results about shifted Schur functions to the general context of shifted Macdonald polynomials. We obtain two explicit formulas for these polynomials: a $q$-integral representation and a combinatorial formula. Our main tool is a $q$-integral representation for ordinary Macdonald polynomials. We also discuss duality for shifted Macdonald polynomials and Jack degeneration of these polynomials.

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BibTeXRIS

Andrei Okounkov. 1997-09-08. (Shifted) Macdonald Polynomials: q-Integral Representation and Combinatorial Formula. https://arxiv.org/abs/q-alg/9605013

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