$p$-kernels occurring in an isogeny class of $p$-divisible groups

We give a criterion which allows to determine, in terms of the combinatorics
of the root system of the general linear group, which p-kernels occur in an
isogeny class of p-divisible groups over an algebraically closed field of
positive characteristic. As an application we obtain a criterion for the
non-emptiness of certain affine Deligne-Lusztig varieties associated to the
general linear group.