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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