Speaker: Caroline Lassueur (Kaiserslautern)
Title: On Character Theory for Endo-Trivial Modules
Abstract:
Let \(k\) be an algebraically closed field of characteristic \(p > 0\) and \(G\) be a finite group of order divisible by \(p\). The aim of this talk is to describe a character-theoretic criterion to detect \(p\)-permutation endo-trivial \(kG\)-modules. When enough information is known about the character table of a group and that of the normaliser of a Sylow \(p\)-subgroup this criterion allows us to recover the full structure of the group of endo-trivial modules. Application to the sporadic groups, the Schur covers of the symmetric and alternating groups, or groups with Klein-four Sylow 2-subgroups will be discussed.