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Séminaire Lotharingien de Combinatoire, B58f (2008), 20 pp.

# Sankaran Viswanath

# 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.

The following versions are available:

**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*.