The McKay—Navarro Conjecture: The Conjecture That Keeps on Giving!

Abstract: The McKay conjecture is one of the main open conjectures in the realm of the local-global philosophy in character theory. It posits a bijection between the set of irreducible characters of a group with p’-degree and the corresponding set in the normalizer of a Sylow p-subgroup. In this talk, I’ll give an overview of a refinement of the McKay conjecture due to Gabriel Navarro, which brings the action of Galois automorphisms into the picture. A lot of recent work has been done on this conjecture, but possibly even more interesting is the amount of information it yields about the character table of a finite group. I’ll discuss some recent results on the McKay—Navarro conjecture, as well as some of the implications the conjecture has had for other interesting character-theoretic problems.

algebraic geometryalgebraic topologygroup theorynumber theoryrepresentation theory

Audience: researchers in the topic

Queen Mary University of London Algebra and Number Theory Seminar