Modular representations of simple Lie algebras

Humphreys, J.

doi:10.1090/S0273-0979-98-00749-6

Modular representations of simple Lie algebras
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Bull. Amer. Math. Soc. 35 (1998), 105-122 Request permission

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.

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