On Cherednik-Macdonald-Mehta identities

1997/12/23 by Pavel Etingof, Alexander Kirillov, Etingof, Pavel +2
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9712051

7 pages, amstex

arxiv created 1997/12/23 · openalex publication_date 1997/12/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we give a short proof of Cherednik's generalization of Macdonald-Mehta identities for the root system A_n-1 using the representation theory of quantum groups. These identities, suggested and proved by Cherednik, give an explicit formula for the integral of a product of Macdonald polynomials with respect to a ``difference analogue of the Gaussian measure''.

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