Kostka-Foulkes polynomials and Macdonald spherical functions
By Kendra Nelsen, Arun Ram. 2004
55 citations recorded by the source corpus.
. Generalized 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 Sch¨utzenberger’s positive formula for the Kostka-Foulkes poynomials in the type A case. field q elements. Hall-Littlewood
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1a47303ee94dae7dbecbd4ba357074c6ec049a91
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Mathematical Physics
Citations in the corpus
- Buildings and Hecke algebras (2006, background): “The main references for this material are [21] and [25].”