Geodesic
Orthogonal subsets of root systems and the orbit method
Algebra i analiz, Tome 22 (2010) no. 5, pp. 104-130.

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Let $k$ be the algebraic closure of a finite field, $G$ a Chevalley group over $k$, $U$ the maximal unipotent subgroup of $G$. To each orthogonal subset $D$ of the root system of $G$ and each set $\xi$ of $|D|$ nonzero scalars in $k$ one can assign the coadjoint orbit of $U$. It is proved that the dimension of such an orbit does not depend on $\xi$. An upper bound for this dimension is also given in terms of the Weyl group.
Keywords: orthogonal subsets of root systems, coadjoint orbits. 
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M. V. Ignat'ev. Orthogonal subsets of root systems and the orbit method. Algebra i analiz, Tome 22 (2010) no. 5, pp. 104-130. http://geodesic.mathdoc.fr/item/AA_2010_22_5_a3/

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