On an asymptotic behavior of elements of order p in irreducible   representations of the classical algebraic groups with large enough highest   weights
  The behavior of the images of a fixed element of order p in irreducible representations of a classical algebraic group in odd characteristic p with highest weights large enough with respect to p and this element is investigated. Lower estimates for the number of Jordan blocks of size p in images of such elements that lie in naturally embedded subgroups of the same type as the initial group and smaller ranks are obtained. 
I.D. Suprunenko (Inst. Math., Natl. Acad. Sci. Belarus)