The Minimal Polynomials of Unipotent Elements in Irreducible Representations of the Special Linear Group

摘要

The minimal polynomials of images of unipotent elements in irreducible rational representations of a special linear group over an algebraically closed field of characteristic p > 2 are found. In particular, we show that the degree of such polynomial is equal to the order of an element provided the highest weight of a representation is in some sense large enough with respect to p.