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Representation Theory

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

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Subregular nilpotent representations of Lie algebras in prime characteristic
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by Jens Carsten Jantzen PDF
Represent. Theory 3 (1999), 153-222 Request permission


We look in this paper at representations of Lie algebras of simple reductive groups in prime characteristic. We investigate those modules that have a subregular nilpotent $p$–character. In case all roots in the corresponding root system have the same length, we determine all simple modules in generic blocks as well as the Cartan matrices of these blocks. Our results confirm conjectures by Lusztig. We determine in these cases also extension groups between non-isomorphic simple modules. There are similar, somewhat less detailed results on non-generic blocks and the cases with two root lengths.
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Additional Information
  • Jens Carsten Jantzen
  • Affiliation: Matematisk Institut, Aarhus Universitet, Ny Munkegade, DK-8000 Aarhus C, Denmark
  • Email:
  • Received by editor(s): May 3, 1999
  • Received by editor(s) in revised form: June 9, 1999
  • Published electronically: July 19, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Represent. Theory 3 (1999), 153-222
  • MSC (1991): Primary 17B10; Secondary 17B20, 17B45, 17B50
  • DOI:
  • MathSciNet review: 1703320