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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Modular representations of simple Lie algebras

Author: J. E. Humphreys
Journal: Bull. Amer. Math. Soc. 35 (1998), 105-122
MSC (1991): Primary 17B20, \; Secondary 20G05
Erratum: Bull. Amer. Math. Soc. 35 (1998), 231.
MathSciNet review: 1605399
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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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J. E. Humphreys
Affiliation: Dept. of Mathematics & Statistics, U. Massachusetts, Amherst, MA 01003-4515

Keywords: Simple Lie algebra, modular representations
Received by editor(s): June 27, 1996
Received by editor(s) in revised form: February 24, 1998
Additional Notes: In preparing this survey I have benefited from extensive correspondence and conversations with Jens Carsten Jantzen, as well as advice from Ivan Mirković and Dmitriy Rumynin.
Dedicated: To the memory of Boris Weisfeiler
Article copyright: © Copyright 1998 American Mathematical Society