Semisimple restrictions from GL(n) to GL(n-1)

We obtain a criterion for the restriction of an irreducible rational GL(n)module to the naturally embedded subgroup GL (n - 1) to be semisimple, over an arbitrary algebraically closed field. In that case, we describe the composition factors of the restriction explicitly. As an application, we classify the completely splittable representations of general linear groups and give an exact character formula for these modules.