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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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

Erratum: Bull. Amer. Math. Soc. 35 (1998), 231.

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.
References
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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
  • 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
  • © Copyright 1998 American Mathematical Society
  • 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
  • MathSciNet review: 1605399