Genotypes of irreducible representations of finite p-groups
Representation Theory
2018-10-01 v1
Abstract
For any characteristic zero coefficient field, an irreducible representation of a finite -group can be assigned a Roquette -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.
Keywords
Cite
@article{arxiv.1809.10957,
title = {Genotypes of irreducible representations of finite p-groups},
author = {Laurence Barker},
journal= {arXiv preprint arXiv:1809.10957},
year = {2018}
}