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28 March 2024
 
  » arxiv » math/0610246

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Kostka-Foulkes polynomials for symmetrizable Kac-Moody algebras
Sankaran Viswanath ;
Date 7 Oct 2006
Subject Representation Theory
AbstractWe 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.
Source arXiv, math/0610246
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