Vector valued Macdonald polynomials

2011/06/05 by Charles F. Dunkl, C. F. Dunkl, Dunkl, C. F. +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA) #Representation Theory (math.RT) #math.CO #math.OA #math.RT

paper · pdf · doi:10.48550/arxiv.1106.0875

85 pages, 5 figures

arxiv created 2011/06/05 · openalex publication_date 2011/06/05 · arxiv updated 2011/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper defines and investigates nonsymmetric Macdonald polynomials with values in an irreducible module of the Hecke algebra of type A_N-1. These polynomials appear as simultaneous eigenfunctions of Cherednik operators. Several objects and properties are analyzed, such as the canonical bilinear form which pairs polynomials with those arising from reciprocals of the original parameters, and the symmetrization of the Macdonald polynomials. The main tool of the study is the Yang-Baxter graph. We show that these Macdonald polynomials can be easily computed following this graph. We give also an interpretation of the symmetrization and the bilinear forms applied to the Macdonald polynomials in terms of the Yang-Baxter graph.

Cited by

• Non-archimedean Infinite Hecke Algebra

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