p‐kernels occurring in an isogeny class of p‐divisible groups

We give a computable 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