Exotic Fourier transform
type: Item
instance of: scholarly article
title: Exotic Fourier transform
zbMATH Open document ID: 0815.20031
DOI: 10.1215/S0012-7094-94-07309-2
author: G. Lusztig
published in: Duke Mathematical Journal
publication date: 1995-07-04T00:00:00Z
review text: A nonabelian Fourier transform for any finite group \(\Gamma\) was introduced by the author [in Q. J. Math., Oxf. II. Ser. 30, 315-338 (1979; Zbl 0418.20038)]. In [\textit{G. Lusztig}, Characters of reductive groups over a finite field (Ann. Math. Stud. 107, 1984; Zbl 0556.20033)] it is stated that the nonabelian Fourier matrices should have a generalization, obtained by allowing the Weyl group to become a noncrystallographic Coxeter group. In the present paper the author describes such a generalization in the case where the ``Weyl group'' is a dihedral group.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 43A30
zbMATH DE Number: 572058
zbMATH Keywords: fusion datum
zbMATH Keywords: matrix representations
zbMATH Keywords: nonabelian Fourier transform
zbMATH Keywords: finite group
zbMATH Keywords: Fourier matrices
zbMATH Keywords: Weyl group
zbMATH Keywords: noncrystallographic Coxeter group
zbMATH Keywords: dihedral group
reviewed by: Vladimir L. Popov
MaRDI profile type: Publication
cites work: Q4279641
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cites work: Characters of Reductive Groups over a Finite Field. (AM-107)
cites work: Q3804915
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cites work: Fusion rules and modular transformations in 2D conformal field theory
description: scientific article; zbMATH DE number 572058