  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.
