Speaker: Sonia Petschick (Wuppertal)
Title: The Galois-McKay Conjecture and Characters of Sylow Normalizers in Special Linear and Special Unitary Groups
Abstract:
A refinement of the McKay Conjecture by Navarro claims that the bijection between the sets of irreducible characters with \(p'\)-degree of \(G\) and the normalizer of a Sylow \(p\)-subgroup is equivariant under certain Galois automorphisms. Similar to the McKay Conjecture, the verification has been reduced to inductive conditions by Navarro, Späth, and Vallejo. I will introduce these inductive conditions and present some progress on their verification for finite groups of type \(A\).