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

Andrei Okounkov

Research output: Contribution to journalArticlepeer-review

43 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)147-182
Number of pages36
JournalCompositio Mathematica
Issue number2
Publication statusPublished - 1998
Externally publishedYes


  • Combinatorial formula
  • Macdonald polynomials
  • q-integral representation
  • Shifted Macdonald polynomials


Dive into the research topics of '(Shipted) Macdonald polynomials: q-Integral representation and combinatorial formula'. Together they form a unique fingerprint.

Cite this