A remark on Fourier pairing and binomial formula for Macdonald polynomials

2001/10/24 by Andrei Okounkov, Andreĭ Okounkov, Okounkov, Andrei
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #math.CO #math.QA

paper · pdf · doi:10.48550/arxiv.math/0110269

11 pages

arxiv created 2001/10/24 · openalex publication_date 2001/10/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a concise direct proof of the orthogonality of interpolation Macdonald polynomials with respect to the Fourier pairing and briefly discuss some immediate applications of this orthogonality, such as the symmetry of the Fourier pairing and the binomial formula.

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• Binomial formula for Macdonald polynomials
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• A combinatorial formula for non-symmetric Macdonald polynomials