Real representation spheres and the real monomial Burnside ring

Date
2012
Authors
Barker, L.
Tuvay, İ.
Advisor
Instructor
Source Title
Journal of Algebra
Print ISSN
0021-8693
Electronic ISSN
218693
Publisher
Elsevior
Volume
353
Issue
1
Pages
79 - 92
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

We introduce a restriction morphism, called the Boltje morphism, from a given ordinary representation functor to a given monomial Burnside functor. In the case of a sufficiently large fibre group, this is Robert Boltje's splitting of the linearization morphism. By considering a monomial Lefschetz invariant associated with real representation spheres, we show that, in the case of the real representation ring and the fibre group {±1}, the image of a modulo 2 reduction of the Boltje morphism is contained in a group of units associated with the idempotents of the 2-local Burnside ring. We deduce a relation on the dimensions of the subgroup-fixed subspaces of a real representation. © 2011 Elsevier Inc.

Course
Other identifiers
Book Title
Keywords
Monomial Lefschetz invariants, Real representation spheres, Real representations of finite groups, primary 20C15, secondary 19A22
Citation
Published Version (Please cite this version)