Young modules for symmetric groups

Let K be a field of characteristic p. The permutation modules associated to partitions of n, usually denoted as M-lambda, play a central role not only for symmetric groups but also for general linear groups, via Schur algebra s. The indecomposable direct summands of these M-lambda were parametrized b y James; they are now known as Young modules; and Klyachko and Grabmeier de veloped a 'Green correspondence' for Young modules. The original parametriz ation used Schur algebras; and James remarked that he did not know a proof using only the representation theory of symmetric groups. We will give such proof, and we will at the same time also prove the correspondence result, by using only the Brauer construction, which is valid for arbitrary finite groups.