Bulletin of the American Mathematical Society

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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Retrieve articles in Bulletin of the American Mathematical Society with MSC (1991): 17B20, \, 20G05

J. E. Humphreys
Affiliation: Dept. of Mathematics & Statistics, U. Massachusetts, Amherst, MA 01003-4515
Email: jeh@math.umass.edu

DOI: 10.1090/S0273-0979-98-00749-6
PII: S 0273-0979(98)00749-6
Keywords: Simple Lie algebra, modular representations
Received by editor(s): June 27, 1996, and in revised form February 24, 1998
Dedicated: To the memory of Boris Weisfeiler
Additional Notes: In preparing this survey I have benefited from extensive correspondence and conversations with Jens Carsten Jantzen, as well as advice from Ivan Mirkovic and Dmitriy Rumynin.
Copyright of article: Copyright 1998, American Mathematical Society

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