A recursion and a combinatorial formula for Jack polynomials
Copyright policy )A recursion and a combinatorial formula for Jack polynomials
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.
Preprint March 1996, to appear in Invent. Math., 15 pages, Plain TeX
- Rutgers, The State University of New Jersey United States
Symmetric functions and generalizations, 05Exx, 33Cxx, Cherednik operators, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), symmetric functions, Jack polynomials, Orthogonal polynomials (combinatorics), tableaux
Symmetric functions and generalizations, 05Exx, 33Cxx, Cherednik operators, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), symmetric functions, Jack polynomials, Orthogonal polynomials (combinatorics), tableaux
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