English

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

q-alg 2016-09-08 v2 Quantum Algebra

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 qq-integral representation and a combinatorial formula. Our main tool is a qq-integral representation for ordinary Macdonald polynomials. We also discuss duality for shifted Macdonald polynomials and Jack degeneration of these polynomials.

Keywords

Cite

@article{arxiv.q-alg/9605013,
  title  = {(Shifted) Macdonald Polynomials: q-Integral Representation and Combinatorial Formula},
  author = {Andrei Okounkov},
  journal= {arXiv preprint arXiv:q-alg/9605013},
  year   = {2016}
}

Comments

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

R2 v1 2026-07-22T19:21:11.492Z