(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.
- Publication:
-
eprint arXiv:q-alg/9605013
- Pub Date:
- May 1996
- DOI:
- 10.48550/arXiv.q-alg/9605013
- arXiv:
- arXiv:q-alg/9605013
- Bibcode:
- 1996q.alg.....5013O
- Keywords:
-
- Mathematics - Quantum Algebra
- E-Print:
- 30 pages, AmS-TeX. Replaced with the journal version. To appear in Comp. Math