Kostka-Foulkes polynomials for symmetrizable Kac-Moody algebras

Details Kostka-Foulkes polynomials for symmetrizable Kac-Moody algebras Kostka-Foulkes polynomials for symmetrizable Kac-Moody algebras

2006-10-07

arxiv.org/abs/math/0610246v2

Seminaire Lotharingien de Combinatoire, 58 (2008), Article B58f

Mathematics

Representation Theory

19 pages

Scientific paper

We introduce a generalization of the classical Hall-Littlewood and Kostka-Foulkes polynomials to all symmetrizable Kac-Moody algebras. 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.

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