(SHIFTED) MACDONALD POLYNOMIALS - Q-INTEGRAL REPRESENTATION AND COMBINATORIAL FORMULA

Authors
OKOUNKOV A
Citation
A. Okounkov, (SHIFTED) MACDONALD POLYNOMIALS - Q-INTEGRAL REPRESENTATION AND COMBINATORIAL FORMULA, Compositio mathematica, 112(2), 1998, pp. 147-182
Citations number
23
Categorie Soggetti
Mathematics,Mathematics
Journal title
Compositio mathematica → ACNP
ISSN journal
0010437X
Volume
112
Issue
2
Year of publication
1998
Pages
147 - 182
Database
ISI
SICI code
0010-437X(1998)112:2<147:(MP-QR>2.0.ZU;2-9
Abstract
We extend some results about shifted Schur functions to the general co ntext of shifted Macdonald polynomials. We strengthen some theorems of F. Knop and S. Sahi and give two explicit formulas for these polynomi als: 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 d egeneration of these polynomials.