A discrete Fourier transform associated with the affine Hecke algebra
type: Item
instance of: scholarly article
title: A discrete Fourier transform associated with the affine Hecke algebra
zbMATH Open document ID: 1246.42006
author: E. Emsiz
author: J. F. Van Diejen
published in: Advances in Applied Mathematics
publication date: 2012-07-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1209.3294
review text: The authors introduce an explicit representation of the double affine Hecke algebra (of type \(A_1\)) at \(q=1\) that gives rise to a periodic counterpart of a well-known Fourier transform associated with the affine Hecke algebra.
reviewed by: Stamatis Koumandos
Mathematics Subject Classification ID: 42A38
Mathematics Subject Classification ID: 20C08
Mathematics Subject Classification ID: 33D80
zbMATH DE Number: 6052930
zbMATH Keywords: discrete Fourier transform
zbMATH Keywords: affine Hecke algebra
zbMATH Keywords: spherical function
MaRDI profile type: Publication
OpenAlex ID: W2047402399
arXiv ID: 1209.3294
cites work: The Fourier transform and the discrete Fourier transform
cites work: Q4067285
cites work: Q4764834
cites work: Q4661506
cites work: Diagonalization of an integrable discretization of the repulsive delta Bose gas on the circle
cites work: Finite-dimensional orthogonality structures for Hall-Littlewood polynomials
cites work: Periodic integrable systems with delta-potentials
cites work: Q4747353
cites work: Fourier transforms related to a root system of rank 1
cites work: Hypergeometric Orthogonal Polynomials and Their q-Analogues
cites work: 𝑞-Krawtchouk polynomials as spherical functions on the Hecke algebra of type 𝐵
cites work: The Askey-Wilson function transform scheme
cites work: Q3136728
cites work: Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
cites work: Q4419564
cites work: Spherical Functions Over -Adic Fields, II
cites work: Q3366978
cites work: Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
cites work: Generalized Lamé functions. I. The elliptic case
cites work: Relativistic Lamé functions: Completeness vs. polynomial asymptotics
cites work: \(PGL_ 2\) over the p-adics: its representations, spherical functions, and Fourier analysis
cites work: The Discrete Cosine Transform
DOI: 10.1016/J.AAM.2011.12.004
description: scientific article; zbMATH DE number 6052930