On vertices of completely splittable modules for symmetric groups and simple modules labelled by two part partitions

摘要

We prove that the vertices of a completely splittable module D for a finite symmetric group over an algebraically closed field of characteristic p > 0 are precisely the defect groups of the block containing D. We also determine the vertices of simple modules for the symmetric groups in characteristic p > 2 which are labelled by two part partitions (n - m, m) such that m < 1/2 p(p + 1).