Fourier transforms and Frobenius eigenvalues for finite Coxeter groups

Meinolf Josef Geck, G. Malle

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Lusztig's classification of the unipotent characters of a finite Chevalley or Steinberg group involves a certain non-abelian Fourier transformation. We construct analogous transformations for the Suzuki and Ree groups, based on a set of axioms derived from Lusztig's theory of character sheaves. We also determine Fourier matrices for the "spetses" (in the sense of Broue, Michel, and the second author) associated with twisted dihedral groups. This completes the determination of Fourier matrices for all "spetses" associated with finite Coxeter groups. We end by collecting common properties of these Fourier matrices and the eigenvalues of Frobenius of character sheaves and unipotent characters. (C) 2003 Elsevier Science (USA). All rights reserved.

Original languageEnglish
Pages (from-to)162-193
Number of pages31
JournalJournal of Algebra
Volume260
Issue number1
DOIs
Publication statusPublished - 2003

Keywords

  • CHARACTER SHEAVES
  • ELEMENTS

Cite this

Fourier transforms and Frobenius eigenvalues for finite Coxeter groups. / Geck, Meinolf Josef; Malle, G.

In: Journal of Algebra, Vol. 260, No. 1, 2003, p. 162-193.

Research output: Contribution to journalArticle

Geck, Meinolf Josef ; Malle, G. / Fourier transforms and Frobenius eigenvalues for finite Coxeter groups. In: Journal of Algebra. 2003 ; Vol. 260, No. 1. pp. 162-193.
@article{97bf946d073a4b3895f7c83fbf5f64ee,
title = "Fourier transforms and Frobenius eigenvalues for finite Coxeter groups",
abstract = "Lusztig's classification of the unipotent characters of a finite Chevalley or Steinberg group involves a certain non-abelian Fourier transformation. We construct analogous transformations for the Suzuki and Ree groups, based on a set of axioms derived from Lusztig's theory of character sheaves. We also determine Fourier matrices for the {"}spetses{"} (in the sense of Broue, Michel, and the second author) associated with twisted dihedral groups. This completes the determination of Fourier matrices for all {"}spetses{"} associated with finite Coxeter groups. We end by collecting common properties of these Fourier matrices and the eigenvalues of Frobenius of character sheaves and unipotent characters. (C) 2003 Elsevier Science (USA). All rights reserved.",
keywords = "CHARACTER SHEAVES, ELEMENTS",
author = "Geck, {Meinolf Josef} and G. Malle",
year = "2003",
doi = "10.1016/S0021-8693(02)00631-2",
language = "English",
volume = "260",
pages = "162--193",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - Fourier transforms and Frobenius eigenvalues for finite Coxeter groups

AU - Geck, Meinolf Josef

AU - Malle, G.

PY - 2003

Y1 - 2003

N2 - Lusztig's classification of the unipotent characters of a finite Chevalley or Steinberg group involves a certain non-abelian Fourier transformation. We construct analogous transformations for the Suzuki and Ree groups, based on a set of axioms derived from Lusztig's theory of character sheaves. We also determine Fourier matrices for the "spetses" (in the sense of Broue, Michel, and the second author) associated with twisted dihedral groups. This completes the determination of Fourier matrices for all "spetses" associated with finite Coxeter groups. We end by collecting common properties of these Fourier matrices and the eigenvalues of Frobenius of character sheaves and unipotent characters. (C) 2003 Elsevier Science (USA). All rights reserved.

AB - Lusztig's classification of the unipotent characters of a finite Chevalley or Steinberg group involves a certain non-abelian Fourier transformation. We construct analogous transformations for the Suzuki and Ree groups, based on a set of axioms derived from Lusztig's theory of character sheaves. We also determine Fourier matrices for the "spetses" (in the sense of Broue, Michel, and the second author) associated with twisted dihedral groups. This completes the determination of Fourier matrices for all "spetses" associated with finite Coxeter groups. We end by collecting common properties of these Fourier matrices and the eigenvalues of Frobenius of character sheaves and unipotent characters. (C) 2003 Elsevier Science (USA). All rights reserved.

KW - CHARACTER SHEAVES

KW - ELEMENTS

U2 - 10.1016/S0021-8693(02)00631-2

DO - 10.1016/S0021-8693(02)00631-2

M3 - Article

VL - 260

SP - 162

EP - 193

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -