q-Difference raising operators for Macdonald polynomials and the integrality of transition coefficients

1996/05/04 by Anatol N. Kirillov, Kirillov, Anatol N., Masatoshi Noumi +1 · 1 citation
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/9605005

openalex publication_date 1996/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study certain q-difference raising operators for Macdonald polynomials (of type A_n-1) which are originated from the q-difference-reflection operators introduced in our previous paper. These operators can be regarded as a q-difference version of the raising operators for Jack polynomials introduced by L.Lapointe and L.Vinet. As an application of our q-difference raising operators we give an elementary proof of the integrality of the double Kostka coefficients which had been conjectured I.G. Macdonald. We also determine their quasi-classical limits, which give rise to (differental) raising operators for Jack polynomials.

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