Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups

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Let Φ be a classical root system and k be a field of sufficiently large characteristic. Let G be the classical group over k with the root system Φ, U be its maximal unipotent subgroup and u be the Lie algebra of U. Let D be an orthogonal subset of Φ and Ω be a coadjoint orbit of U associated with D. We construct a polarization of u at the canonical form on Ω. We also find the dimension of Ω in terms of the Weyl group of Φ. As a corollary, we determine all possible dimensions of irreducible complex represenations of the group U for the case of finite field k.