Séminaire Lotharingien de Combinatoire, B58f (2008), 20 pp.
Kostka-Foulkes Polynomials for Symmetrizable Kac-Moody Algebras
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
g be simply-laced.