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