Integrality of two variable Kostka functions

Knop F (1997)


Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 1997

Journal

Publisher: Walter de Gruyter

Book Volume: 482

Pages Range: 177-189

DOI: 10.1515/crll.1997.482.177

Abstract

Macdonald defined a family of symmetric polynomials which depend on two parameters q and t. The coefficients of the transition matrix from Macdonald polynomials to Schur S-functions are called Kostka functions. Macdonald conjectured that they are polynomials in q and t with non-negative integers as coefficients. In the paper I prove that the Kostka functions are polynomials with integral coefficients. The positivity part remains open.

The proof uses a non-symmetric analogue of Macdonald polynomials (also introduced by Macdonald). I derive a recursion formula for them and a formula relating the symmetric with the non-symmetric Macdonald polynomials. I also define a non-symmetric analogue of Hall-Littlewood polynomials and use them to state and prove an integrality result for the non-symmetric Macdonald polynomials. This implies integrality of Kostka functions.

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How to cite

APA:

Knop, F. (1997). Integrality of two variable Kostka functions. Journal für die reine und angewandte Mathematik, 482, 177-189. https://dx.doi.org/10.1515/crll.1997.482.177

MLA:

Knop, Friedrich. "Integrality of two variable Kostka functions." Journal für die reine und angewandte Mathematik 482 (1997): 177-189.

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