Nikolaus Conference 2023

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, Sp├Ąth, and Vallejo. I will introduce these inductive conditions and present some progress on their verification for finite groups of type \(A\).

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