London Algebra Colloquium abstract

Minimal non-zero heights of irreducible characters

Charles Eaton (Manchester), 19th November 2009

Abstract

A famous conjecture of Brauer states that a block has abelian defect groups if and only if every irreducible character in that block has height zero (for the principal block this means that the Sylow p-subgroups are abelian if and only if every irreducible character has degree prime to p). In joint work with Alexander Moreto, we consider the non-abelian defect group case and examine the relationship between the smallest positive height for irreducible characters in a block and the defect group. Dade’s conjecture turns out to play an important rôle.