Genotypes of irreducible representations of finite p-groups

QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...

Finite p-groups with few non-linear irreducible character kernels

Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

K-theory, genotypes, and biset functors

Let p be an odd prime number. In this paper, we show that the genome Γ(P ) of a finite p-group P , defined as the direct product of the genotypes of all rational irreducible representations of P , can be recovered from the first group of K-theory K1(QP ). It follows that the assignment P 7→ Γ(P ) is a p-biset functor. We give an explicit formula for the action of bisets on Γ, in terms of genera...

Proving Admissibility of Irreducible Unitaries

• Higher commutators • Godement’s principle: bounding dimensions of irreducibles • The von Neumann (strong) density theorem • Lie’s Theorem on irreducible finite-dimensional representations of connected solvable groups • Separating families of irreducible finite-dimensional representations • Subrepresentation Theorem for finite-dimensional representations of reductive linear real Lie groups • T...

On Finite Groups With Two Irreducible Character Degrees