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 {L _i }| ^pn−2 _{i =−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 . Received May 10, 1999, Accepted December 8, 1999