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28 March 2024
 
  » arxiv » math.RT/0401298

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Kostka-Foulkes polynomials and Macdonald spherical functions
Kendra Nelsen ; Arun Ram ;
Date 22 Dec 2003
Journal Surveys in Combinatorics 2003 , C. Wensley ed., London Math. Soc. Lect. Notes 307, Cambridge University Press, 2003, 325--370.
Subject Representation Theory; Combinatorics; Quantum Algebra | math.RT math.CO math.QA
AbstractGeneralized Hall-Littlewood polynomials (Macdonald spherical functions) and generalized Kostka-Foulkes polynomials ($q$-weight multiplicities) arise in many places in combinatorics, representation theory, geometry, and mathematical physics. This paper attempts to organize the different definitions of these objects and prove the fundamental combinatorial results from ``scratch’’, in a presentation which, hopefully, will be accessible and useful for both the nonexpert and researchers currently working in this very active field. The combinatorics of the affine Hecke algebra plays a central role. The final section of this paper can be read independently of the rest of the paper. It presents, with proof, Lascoux and Schützenberger’s positive formula for the Kostka-Foulkes poynomials in the type A case.
Source arXiv, math.RT/0401298
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