Prehomogeneous Spaces for the Coadjoint Action of a Parabolic Group
نویسنده
چکیده
Let k be an algebraically closed field and let G be a reductive linear algebraic group over k. Let P be a parabolic subgroup of G, Pu its unipotent radical and pu the Lie algebra of Pu. A fundamental result of R. Richardson says that P acts on pu with a dense orbit (see [9]). The analogous result for the coadjoint action of P on pu is already known for char k = 0 (see [5]). In this note we prove this result for arbitrary characteristic. Our principal result is that bu is a prehomogeneous space for a Borel subgroup B of G. From this we deduce that a parabolic subgroup P of G acts on n∗ with a dense orbit for any P -submodule n of P . Further, we determine when the orbit map for such an orbit is separable.
منابع مشابه
Maximal prehomogeneous subspaces on classical groups
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