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

Nevins, Monica

doi:10.1090/S1088-4165-02-00134-6

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

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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