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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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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


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:
  • 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:
  • MathSciNet review: 1605399