(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

References in corpus (3)

• Difference equations and symmetric polynomials defined by their zeros
• Symmetric and non-symmetric quantum Capelli polynomials
• Young Basis, Wick Formula, and Higher Capelli Identities

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• LU factorizations, q=0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials
• Interpolation analogues of Schur Q-functions
• A generalization of Newton's identity and Macdonald functions
• Macdonald polynomials and extended Gelfand-Tsetlin graph