Speaker: Annika Bartelt (Kaiserslautern)
Title: Character Degrees in Principal Blocks of Classical Groups of Lie Type for Distinct Primes
Abstract:
A conjecture of Navarro, Rizo and Schaeffer Fry (2022) relates the existence of a Hall \(\{p,q\}\)-subgroup of a finite group \(G\) to the absence of certain characters of \(G\). The characters under consideration lie in both principal blocks for two distinct primes \(p\) and \(q\) and have degree prime to \(p\) and \(q\). They reduced their conjecture to a problem on almost simple groups and proved it in some cases. In this talk, we consider the open case of simple classical groups of Lie type, where \(p\) and \(q\) are two distinct non-defining (odd) primes. The approach relies on the combinatorics of their unipotent characters.