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
DOI:
https://doi.org/10.1090/S0273-0979-98-00749-6
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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Additional Information
J. E. Humphreys
Affiliation:
Dept. of Mathematics & Statistics, U. Massachusetts, Amherst, MA 01003-4515
Email:
jeh@math.umass.edu
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