Induced representations of double affine Hecke algebras and applications
type: Item
instance of: scholarly article
title: Induced representations of double affine Hecke algebras and applications
zbMATH Open document ID: 0837.20052
published in: Mathematical Research Letters
publication date: 1995-11-16T00:00:00Z
review text: The main results (Cherednik, 1991-1993) about the structure of double affine Hecke algebras are applied to induced representations. The technique used is based on the theory of Weyl groups, the matrix Demazure-Lusztig operators and the difference-matrix counterparts of the operators (Heckman, 1991; Opdam, 1989). The Hecke algebra and its affine extensions are introduced by starting from a given root system. It is proved the difference version of the generalized Matsuo (1991) theorem which gives an isomorphism between the affine Knizhnik-Zamolodchikov (AKZ) equation and the eigenvalue problem (SHOHS) for operators unifying the Sutherland-Heckman-Opdam and Haldany-Shastry ones. As a result, the equivalence of the difference SHOHS with the values in an arbitrary representation of the Hecke algebra and the difference AKZ considered in the corresponding induced representation of the affine Hecke algebra is established (Theorem 4.3). The AKZ equation is connected with Smirnov- Frenkel-Reshetikhin equations for the simplest tensor products. The scalar version of above theorem is directly related to the Macdonald theory (1988).
Mathematics Subject Classification ID: 20C08
Mathematics Subject Classification ID: 39A70
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 17B22
Mathematics Subject Classification ID: 33D52
zbMATH DE Number: 817698
zbMATH Keywords: double affine Hecke algebras
zbMATH Keywords: induced representations
zbMATH Keywords: Weyl groups
zbMATH Keywords: Demazure-Lusztig operators
zbMATH Keywords: tensor products
author: Ivan Cherednik
reviewed by: A. A. Bogush
MaRDI profile type: Publication
full work available at URL: mrl.1994.v1.n3.a4
OpenAlex ID: W2018743078
DOI: 10.4310/MRL.1994.V1.N3.A4
description: scientific article; zbMATH DE number 817698