Speaker: Caroline Lassueur (Hannover)
Title: On the Type of the Self-Dual Indecomposable Modules in Positive Characteristic
Abstract:
Let \(p\) be an odd prime and let \(B\) be a self-dual \(p\)-block of a finite group. We consider the following question: Can we describe the self-dual indecomposable \(B\)-modules and for each such module determine its type, that is, whether it is symplectic or orthogonal? The type is not invariant under Morita equivalences. However, we show that for the special case of blocks with cyclic defect groups, the type can be read off from the embedded Brauer tree, provided the type of one simple \(B\)-module is known. This answers a question of John Murray.