Genotypes of irreducible representations of finite p-groups
Date
2006-12-15
Authors
Barker, L.
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Source Title
Journal of Algebra
Print ISSN
0021-8693
Electronic ISSN
1090-266X
Publisher
Academic Press
Volume
306
Issue
2
Pages
655 - 681
Language
English
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Journal Title
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Abstract
For any characteristic zero coefficient field, an irreducible representation of a finite p-group can be assigned a Roquette p-group, called the genotype. This has already been done by Bouc and Kronstein in the special cases Q and C. A genetic invariant of an irrep is invariant under group isomorphism, change of coefficient field, Galois conjugation, and under suitable inductions from subquotients. It turns out that the genetic invariants are precisely the invariants of the genotype. We shall examine relationships between some genetic invariants and the genotype. As an application, we shall count Galois conjugacy classes of certain kinds of irreps. © 2006 Elsevier Inc. All rights reserved.