Kostka–foulkes Polynomials for Symmetrizable Kac–moody Algebras

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.