Towards spetses. I
type: Item
instance of: scholarly article
title: Towards spetses. I
zbMATH Open document ID: 0972.20024
DOI: 10.1007/BF01237357
author: Jean Michel
author: Michel Broué
author: Gunter Malle
published in: Transformation Groups
publication date: 2001-06-19T00:00:00Z
review text: Rational reflection groups occur naturally as Weyl groups of reductive algebraic groups over finite fields. The authors conjecture that complex reflection groups are similarly related to some as yet undiscovered objects which they call spetses. To prepare the search for spetses, the authors collect technical results on many subjects like braid groups, generic Hecke algebras, reflection data, cyclotomic specializations of Hecke algebras, spetsial cyclotomic Hecke algebras. They obtain families of unipotent characters for spetses.
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20C08
zbMATH DE Number: 1347435
zbMATH Keywords: spetses
zbMATH Keywords: unipotent characters
zbMATH Keywords: Hecke algebras
zbMATH Keywords: braid groups
zbMATH Keywords: reflection groups
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
cites work: Representation theory of a Hecke algebra of \(G(r,p,n)\)
cites work: A Hecke algebra of \((\mathbb{Z}/r\mathbb{Z})\wr{\mathfrak S}_ n\) and construction of its irreducible representations
cites work: Schur indices and splitting fields of the unitary reflection groups
cites work: Sur le corps de définition d'un groupe de réflexions complexe
cites work: Reduced words and a length function for \(G(e,1,n)\)
cites work: Q4866210
cites work: Generic Sylow theorems for the reductive groups over finite fields
cites work: Q4279641
cites work: Q4279639
cites work: Q4398664
cites work: Invariants of Finite Groups Generated by Reflections
cites work: Finite complex reflection groups
cites work: Q5688170
cites work: Q4263822
cites work: Characters of Reductive Groups over a Finite Field. (AM-107)
cites work: Q4279642
cites work: Unipotent degrees of imprimitive complex reflection groups
cites work: Symmetric cyclotomic Hecke algebras
cites work: A remark on the irreducible characters and fake degrees of finite real reflection groups
cites work: Combinatorics and topology of complements of hyperplanes
cites work: Unitary reflection groups and cohomology
cites work: Q4003206
cites work: Characterization of characters and pseudo-characters
cites work: Finite Unitary Reflection Groups
cites work: Regular elements of finite reflection groups
cites work: Differential Equations Invariant Under Finite Reflection Groups
description: scientific article; zbMATH DE number 1347435