Real representation spheres and the real monomial Burnside ring

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

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