The McKay conjecture and Galois automorphisms


The main problem of representation theory of finite groups is to find proofs of several conjectures stating that certain global invariants of a finite group $G$ can be computed locally. The simplest of these conjectures is the “McKay conjecture” which asserts that the number of irreducible complex characters of $G$ of degree not divisible by $p$ is the same if computed in a $p$-Sylow normalizer of $G$. In this paper, we propose a much stronger version of this conjecture which deals with Galois automorphisms. In fact, the same idea can be applied to the celebrated Alperin and Dade conjectures.


Gabriel Navarro

Facultat de Ciències Matemàtiques, Universitat de València, València, Spain