Some integral representations of complex reflection groups
type: Item
instance of: scholarly article
title: Some integral representations of complex reflection groups
zbMATH Open document ID: 1027.20003
DOI: 10.1016/S0021-8693(02)00629-4
author: Walter Feit
published in: Journal of Algebra
publication date: 2003-04-28T00:00:00Z
review text: Let \(G\) be a finite unitary group generated by complex reflections. The group \(G\) consists of matrices generated by complex reflections. Let \(F\) be a field containing \(\mathbb{Q}(G)\). Let \(R\) be the ring of integers in \(F\). Then \(G\) can be written as a group of matrices with entries in \(R\). Such a representation of \(G\) is called a reflection representation of \(G\). Let \(N(G,F)\) denote the number of \(R\)-equivalence classes of \(R\)-representations of \(G\) which are \(F\)-equivalent to a reflection representation. Let \(N(G)=N(G,\mathbb{Q}(G))\). The paper is devoted to the calculation of \(N(G)\) for all types of finite unitary groups generated by complex reflections.
Mathematics Subject Classification ID: 20C10
Mathematics Subject Classification ID: 20F55
zbMATH DE Number: 1901820
zbMATH Keywords: complex reflection groups
zbMATH Keywords: integral representations
zbMATH Keywords: lattices
zbMATH Keywords: finite unitary groups
zbMATH Keywords: reflection representations
reviewed by: Kanat Abdukhalikov
MaRDI profile type: Publication
cites work: Schur indices and splitting fields of the unitary reflection groups
cites work: Q5580319
cites work: Finite complex reflection groups
cites work: A characterization of certain extreme forms
cites work: Integral representations of Weyl groups rationally equivalent to the reflection representation
cites work: Q4693118
cites work: The crystallography of Coxeter groups
cites work: The root lattices of the complex reflection groups
cites work: Finite Unitary Reflection Groups
Recommended article: Q4518768
Recommended article: Some graded representations of the complex reflection groups
Recommended article: Complex reflection groups
Recommended article: Integral representations of Weyl groups rationally equivalent to the reflection representation
Recommended article: Integral representations for the alternating groups
Recommended article: Q3987893
Recommended article: Q4852725
Recommended article: Q3483471
Recommended article: Integral representations of finite transformation groups. I
Recommended article: Representations of the imprimitive complex reflection groups G(m, 1n)
description: scientific article; zbMATH DE number 1901820