Integrality of two variable Kostka functions

Details Integrality of two variable Kostka functions Integrality of two variable Kostka functions

1996-03-29

arxiv.org/abs/q-alg/9603027v1

J. Reine Angew. Math. 482 (1997), 177-189

Mathematics

Quantum Algebra

14 pages

Scientific paper

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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