A recursion and a combinatorial formula for Jack polynomials

Knop F, Sahi S (1997)

Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 1997

Journal

Inventiones Mathematicae Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 128

Pages Range: 9-22

Journal Issue: 1

DOI: 10.1007/s002220050134

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.

Authors with CRIS profile

Friedrich Knop Lehrstuhl für Mathematik (Algebra und Geometrie)

How to cite

APA:

Knop, F., & Sahi, S. (1997). A recursion and a combinatorial formula for Jack polynomials. Inventiones Mathematicae, 128(1), 9-22. https://dx.doi.org/10.1007/s002220050134

MLA:

Knop, Friedrich, and Siddhartha Sahi. "A recursion and a combinatorial formula for Jack polynomials." Inventiones Mathematicae 128.1 (1997): 9-22.

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