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

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

1996-05-09

arxiv.org/abs/q-alg/9605013v2

Mathematics

Quantum Algebra

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

Scientific paper

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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