Orthogonal subsets of root systems and the orbit method

Original · EN

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 the group G and each set ξ of |D| non-zero scalars from k one can assign the coadjoint orbit of the group U. We prove that the dimension of such an orbit does not depend on ξ. We also give an upper bound of the dimension in terms of the Weyl group.