Yang-Baxter Graphs, Jack and Macdonald Polynomials

Abstract. 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.

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