%0 Journal Article
%T Polynomiality of the q,t-Kostka Revisited
%A A. M. Garsia
%A Mike Zabrocki
%J Mathematics
%D 2000
%I arXiv
%X Let $K(q,t)= \|K_{\la\mu}(q,t)\|_{\la,\mu}$ be the Macdonald q,t-Kostka matrix and $K(t)=K(0,t)$ be the matrix of the Kostka-Foulkes polynomials K_{\la\mu}(t). In this paper we present a new proof of the polynomiality of the q,t-Kostka coefficients that is both short and elementary. More precisely, we derive that $K(q,t)$ has entries in \ZZ[q,t] directly from the fact that the matrix $K(t)^{-1}$ has entries in \ZZ[t]. The proof uses only identities that can be found in the original paper [7] of Macdonald.
%U http://arxiv.org/abs/math/0008199v1