Brauer homomorphism and simple modules

Hey there,

several weeks ago, there was a discussion on the Brauer hom (see Is the Brauer correspondence injective ? ). I like to investigate this hom when being applied to simple modules: Let $k$ be an alg. closed field of positive characteristic and let $G$ be a finite group. Assume that $P$ is a $p$-subgroup of $G$. What can be said about the image of the Brauer hom on a simple $kG$-module $S$ with vertex $P$, i.e. what can be said about $Br_P(S):=\frac{S^P}{\sum_{Q<P}tr^P_Q(S^Q)}$, where $S^Q$ denotes the $Q$-invariants of $S$ and $tr^P_Q:S^Q\rightarrow S^P, x\mapsto \sum_{g\in P/Q}gx$ denotes the trace map. Does the fact that $S$ is simple add any properties to the image as for instance indecomposable modules with trivial source do?

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I think this question has been considered by P.J. Webb in connection with Mackey functors. – Geoff Robinson Aug 30 '12 at 4:53