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Integrality of two variable Kostka functions

Friedrich Knop
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Abstract

The two variable Kostka functions are the scalar products of the Macdonald polynomials with the Schur polynomials with respect to the scalar product which makes the Hall-Littlewood polynomials pairwise orthogonal. A conjecture of Macdonald states that they are polynomials in q and t with non-negative integral coefficients. We prove that the Kostka functions are at least polynomials with integral coefficients. The main idea is to prove an analogous statement for the non-symmetric Macdonald polynomials by establishing recursion relations via the affine Hecke algebra.

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Friedrich Knop. 1996-03-29. Integrality of two variable Kostka functions. https://doi.org/10.1515/crll.1997.482.177

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