Conjugation in Representations of the Zassenhaus Algebra

Let F be an algebracially closed field of characteristic p > 2, and L be the p n-dimensional Zassenhaus algebra with the maximal invariant subalgebra L 0 and the standard filtration {Li}pn2i=1. Then the number of isomorphism classes of simple L-modules is equal to that of simple L 0-modules, corresponding to an arbitrary character of L except when its height is biggest. As to the number corresponding to the exception there was an earlier result saying that it is not bigger than p n.