Positive representations of finite groups in Riesz spaces

Details Positive representations of finite groups in Riesz spaces Positive representations of finite groups in Riesz spaces

2011-09-21

arxiv.org/abs/1109.4505v3

Mathematics

Functional Analysis

23 pages. To appear in International Journal of Mathematics

Scientific paper

In this paper, which is part of a study of positive representations of locally compact groups in Banach lattices, we initiate the theory of positive representations of finite groups in Riesz spaces. 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. We 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 turns out not to hold.

Affiliated with

Also associated with

No associations

Rating

Positive representations of finite groups in Riesz spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Positive representations of finite groups in Riesz spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positive representations of finite groups in Riesz spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-257193