Modular representations of simple Lie algebras
J. E. Humphreys
Dept. of Mathematics & Statistics, U. Massachusetts, Amherst, MA 01003-4515 
Bull. Amer. Math. Soc. 35 (1998), pp. 105-122.

Abstract. In spite of many efforts over the past 50 years, the irreducible 
representations of the Lie algebra of a simple algebraic group over a field 
of prime characteristic are poorly understood. Recent work on quantum groups 
at a root of unity has provided new impetus for the subject. This article 
surveys what has been done and what remains to be done. 

In preparing this survey I have benefited from extensive correspondence and 
conversations with Jens Carsten Jantzen, as well as advice from Ivan
Mirkovi\'{c} and Dmitriy Rumynin. To the memory of Boris Weisfeiler.