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

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.

30 pages, AmS-TeX. Replaced with the journal version. To appear in Comp. Math