A recursion and a combinatorial formula for Jack polynomials
Abstract
Heckman and Opdam introduced a non-symmetric analogue of Jack polynomials using Cherednik operators. In this paper, we derive a simple recursion formula for these polynomials and formulas relating the symmetric Jack polynomials with the non-symmetric ones. These formulas are then implemented by a closed expression of symmetric and non-symmetric Jack polynomials in terms of certain tableaux. The main application is a proof of a conjecture of Macdonald stating certain integrality and positivity properties of Jack polynomials.
- Publication:
-
Inventiones Mathematicae
- Pub Date:
- March 1997
- DOI:
- 10.1007/s002220050134
- arXiv:
- arXiv:q-alg/9610016
- Bibcode:
- 1997InMat.128....9K
- Keywords:
-
- Mathematics - Quantum Algebra;
- 05Exx;
- 33Cxx
- E-Print:
- Preprint March 1996, to appear in Invent. Math., 15 pages, Plain TeX