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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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Admissible nilpotent orbits of real and $p$-adic split exceptional groups
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by Monica Nevins PDF
Represent. Theory 6 (2002), 160-189 Request permission


We determine the admissible nilpotent coadjoint orbits of real and $p$-adic split exceptional groups of types $G_2$, $F_4$, $E_6$ and $E_7$. We find that all Lusztig-Spaltenstein special orbits are admissible. Moreover, there exist non-special admissible orbits, corresponding to “completely odd” orbits in Lusztig’s special pieces. In addition, we determine the number of, and representatives for, the non-even nilpotent $p$-adic rational orbits of $G_2$, $F_4$ and $E_6$.
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Additional Information
  • Monica Nevins
  • Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ontario, Canada K1N 6N5
  • Email:
  • Received by editor(s): July 13, 2001
  • Received by editor(s) in revised form: April 16, 2002
  • Published electronically: August 7, 2002
  • Additional Notes: The author was supported in part by the Killam Trust, and by NSERC of Canada grant RGPIN229816.
  • © Copyright 2002 American Mathematical Society
  • Journal: Represent. Theory 6 (2002), 160-189
  • MSC (2000): Primary 20G25; Secondary 17B20, 17B45
  • DOI:
  • MathSciNet review: 1915090