Genotypes of irreducible representations of finite p-groups

2018/09/28 by Laurence Barker, Barker, Laurence
Computer Science · Engineering · Mathematics · #20C15 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #graph theory and CDMA systems #math.RT #msc:20C15

paper · pdf · doi:10.48550/arxiv.1809.10957

arxiv created 2018/09/28 · openalex publication_date 2018/09/28 · arxiv updated 2018/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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