Abstract: | Two theorems about the vertices of indecomposable Specht modules for the
symmetric group, defined over a field of prime characteristic p, are
proved:
1. The indecomposable Specht module $S^\lambda$ has non-trivial cyclic vertex
if and only if $\lambda$ has p-weight 1.
2. If p does not divide n and $S^{(n-r, 1^r)}$ is indecomposable then
its vertex is a p-Sylow subgroup of $S_{n-r-1} \times S_r$.Received: 15 August 2002 |