Semisimple restrictions from GL(n) to GL(n-1)
Jonathan Brundan, Alexander Kleshchev and Irina Suprunenko

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.