Integrality of two variable Kostka functions

Knop F (1997)

Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 1997


Publisher: Walter de Gruyter

Book Volume: 482

Pages Range: 177-189

DOI: 10.1515/crll.1997.482.177


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.

Authors with CRIS profile

How to cite


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


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

BibTeX: Download