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(Shifted) Macdonald polynomials: q-Integral representation and combinatorial formula

Published online by Cambridge University Press:  04 December 2007

ANDREI OKOUNKOV
ANDREI OKOUNKOV
Affiliation:
Department of Mathematics, University of Chicago, 5734 South University Avenue, Chicago, IL 60637-1546, U.S.A. e-mail: okounkovmath.unchicago.edu
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Abstract

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We extend some results about shifted Schur functions to the general context of shifted Macdonald polynomials. We strengthen some theorems of F. Knop and S. Sahi and give 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 polynomial. We also discuss duality for shifted Macdonald polynomials and Jack degeneration of these polynomials.

Keywords

Macdonald polynomialsshifted Macdonald polynomialscombinatorial formulaq-integral representation.
Type
Research Article
Information
Compositio Mathematica , Volume 112 , Issue 2 , June 1998 , pp. 147 - 182
Copyright
© 1998 Kluwer Academic Publishers