Positive representations of finite groups in Riesz spaces.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1259.20011
DOI: 10.1142/S0129167X12500760
author: Marten Wortel
author: Marcel de Jeu
published in: International Journal of Mathematics
publication date: 2012-08-30T00:00:00Z
full work available at URL: https://arxiv.org/abs/1109.4505
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 22D12
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 06F20
zbMATH DE Number: 6074252
zbMATH Keywords: finite groups
zbMATH Keywords: positive representations
zbMATH Keywords: order indecomposable representations
zbMATH Keywords: irreducible representations
zbMATH Keywords: vector lattices
zbMATH Keywords: Riesz spaces
zbMATH Keywords: Banach lattices
zbMATH Keywords: representations of locally compact groups
MaRDI profile type: Publication
arXiv ID: 1109.4505
cites work: Q5638775
cites work: Linearly equivalent actions of solvable groups
cites work: Counterexamples in topology
title: Positive representations of finite groups in Riesz spaces.
review text: The authors initiate the theory of positive representations of finite groups in Banach lattices. If such a representation has only the zero subspace and possibly the space itself as invariant principal bands, then the space is Archimedean and finite dimensional. Various notions of irreducibility of a positive representation are introduced and, for a finite group acting positively in a space with sufficiently many projections, these are shown to be equal. They describe the finite dimensional positive Archimedean representations of a finite group and establish that, up to order equivalence, these are order direct sums, with unique multiplicities, of the order indecomposable positive representations naturally associated with transitive G-spaces. Character theory is shown to break down for positive representations. Induction and systems of imprimitivity are introduced in an ordered context, where the multiplicity formulation of Frobenius reciprocity is shown not to hold.
reviewed by: Şafak Alpay
description: scientific article; zbMATH DE number 6074252