Representation-theoretic proof of the inner product and symmetry identities for MacDonald's polynomials

1994/11/30 by Pavel Etingof, Alexander Kirillov, Etingof, Pavel I. +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.math/9411232

openalex publication_date 1994/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This paper is a continuation of our papers [EK1, EK2]. In [EK2] we showed that for the root system A_n-1 one can obtain Macdonald's polynomials - a new interesting class of symmetric functions recently defined by I. Macdonald M1] - as weighted traces of intertwining operators between certain finite-dimensional representations of U_q sl_n. The main goal of the present paper is to use this construction to give a representation-theoretic proof of Macdonald's inner product and symmetry identities for the root system A_n-1. Macdonald's inner product identities (see [M2]) have been proved by combinatorial methods my Macdonald ([Macdonald, private communication]).

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