A reproducing kernel for nonsymmetric Macdonald polynomials

1996/10/11 by Katsuhisa Mimachi, Mimachi, K., Masatoshi Noumi +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.q-alg/9610014

openalex publication_date 1996/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a new formula of Cauchy type for the nonsymmetric Macdonald polynomials which are joint eigenfunctions of q-Dunkl operators. This gives the explicit formula for a reproducing kernel on the polynomial ring of n variables.

Cited by

• Isomorphisms of type A affine Hecke algebras and multivariable orthogonal polynomials
• Shuffle algebras, lattice paths and quantum toroidal \mathfrakgl_n|m

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