# Kostka-Foulkes Polynomials for Symmetrizable Kac-Moody Algebras

Abstract. We introduce a generalization of the classical Hall-Littlewood and Kostka-Foulkes polynomials to all \skmas. We prove that these Kostka-Foulkes polynomials coincide with the natural generalization of Lusztig's t-analog of weight multiplicities, thereby extending a theorem of Kato. For g an affine Kac-Moody algebra, we define t-analogs of string functions and use Cherednik's constant term identities to derive explicit product expressions for them.

Received: August 28, 2007. Accepted: October 6, 2008. Final Version: October 24, 2008.

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Erratum: The statements of Theorems 2, 3 and Corollary 3 (pages 12, 13, 14) must include the hypothesis that the affine Kac-Moody algebra g be simply-laced.