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Yang-Baxter Graphs, Jack and Macdonald Polynomials
Alain Lascoux
CNRS, Institut Gaspard Monge, Université de Marne-la-Vallée 77454 Marne-la-Vallée Cedex, France
Annals of Combinatorics 5 (3) p.397-424 September, 2001
AMS Subject Classification: 05E05
We describe properties of the affine graph underlying the recursions between the different varieties of nonsymmetric Macdonald and Jack polynomials. We use an arbitrary function of one variable in the definition of affine edges, and of Cherednik's elements, to unify the different theories. We describe the symmetrizing operators furnishing the symmetric polynomials from the nonsymmetric ones.
Keywords: Macdonald polynomials, Jack polynomials, Yang-Baxter


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