Modules with simple multiplicity modules
Let \(G\) be a finite group, \(\mathcal O\) be a complete local commutative noetherian ring with an algebraically closed residue field \(k\) of nonzero characteristic \(p\). Let \(M\) be an indecomposable \({\mathcal O}G\)-module with vertex \(P\), \(\delta\) be a local point of \(P\) on \(\text{End}_{\mathcal O}(M)\) and \(V\) be the multiplicity \(k_*\widehat{\overline {N}}_G(P_\delta)\)-module of \(M\). In Section 1 the author gives some necessary and sufficient criteria for \(V\) to be simple. In Section 2 the author presents a reciprocity law which concerns direct summands of modules induced from, and modules restricted from, modules with simple multiplicity modules.
scientific article; zbMATH DE number 763913