Geodesic
Kostka-Foulkes Polynomials for Symmetrizable Kac-Moody Algebras
Séminaire lotharingien de combinatoire, Tome 58 (2007-2008)

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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.

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. 
@article{SLC_2007-2008_58_a5,
     author = {Sankaran Viswanath},
     title = {Kostka-Foulkes {Polynomials} for {Symmetrizable} {Kac-Moody} {Algebras}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {58},
     year = {2007-2008},
     url = {http://geodesic.mathdoc.fr/item/SLC_2007-2008_58_a5/}
}
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Sankaran Viswanath. Kostka-Foulkes Polynomials for Symmetrizable Kac-Moody Algebras. Séminaire lotharingien de combinatoire, Tome 58 (2007-2008). http://geodesic.mathdoc.fr/item/SLC_2007-2008_58_a5/