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Let $k$ be the algebraic closure of a finite field, $G$ a Chevalley groupover $k$, $U$ the maximal unipotent subgroup of $G$. To each orthogonal subset$D$ of the root system of the group $G$ and each set $\xi$ of $|D|$ non-zeroscalars from $k$ one can assign the coadjoint orbit of the group $U$. We provethat the dimension of such an orbit does not depend on $\xi$. We also give anupper bound of the dimension in terms of the Weyl group.

Orthogonal subsets of root systems and the orbit method