Brauer Theory for Profinite Groups

John MacQuarrie; Peter Symonds

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arXiv · 1301.5625

Brauer Theory for Profinite Groups

John MacQuarrie·Peter Symonds

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Abstract

Brauer Theory for a finite group can be viewed as a method for comparing the representations of the group in characteristic 0 with those in prime characteristic. Here we generalize much of the machinery of Brauer theory to the setting of profinite groups. By regarding Grothendieck groups as functors we describe corresponding Grothendieck groups for profinite groups, and generalize the decomposition map, regarded as a natural transformation. We discuss characters and Brauer characters for profinite groups. We give a functorial description of the block theory of a profinite group. We finish with a method for computing the Cartan matrix of a finite group $G$ given the Cartan matrix for a quotient of $G$ by a normal $p$-subgroup.

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BibTeX RIS

John MacQuarrie, Peter Symonds. 2013-01-23. Brauer Theory for Profinite Groups. https://arxiv.org/abs/1301.5625

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