Orthogonal Subsets of Root Systems and the Orbit Method

@inproceedings{IGNATEV2011OrthogonalSO,
  title={Orthogonal Subsets of Root Systems and the Orbit Method},
  author={M. V. IGNAT′EV},
  year={2011}
}
  • M. V. IGNAT′EV
  • Published 2011
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 ξ 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 ξ. An upper bound for this dimension is also given in terms of the Weyl group.