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Admissible nilpotent orbits of real and $p$-adic split exceptional groups


Author: Monica Nevins
Journal: Represent. Theory 6 (2002), 160-189
MSC (2000): Primary 20G25; Secondary 17B20, 17B45
DOI: https://doi.org/10.1090/S1088-4165-02-00134-6
Published electronically: August 7, 2002
MathSciNet review: 1915090
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Abstract: 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: mnevins@uottawa.ca

DOI: https://doi.org/10.1090/S1088-4165-02-00134-6
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.
Article copyright: © Copyright 2002 American Mathematical Society