Prehomogeneous spaces for parabolic group actions in classical groups

Goodwin, Simon and Roehrle, Gerhard (2004) Prehomogeneous spaces for parabolic group actions in classical groups. Journal of Algebra, 276 (1), 383-398. (doi:10.1016/j.jalgebra.2003.11.005).

Abstract

Let G be a reductive linear algebraic group, P a parabolic subgroup of G and Pu its unipotent radical. We consider the adjoint action of P on the Lie algebra of Pu. Richardson's dense orbit theorem says that there is a dense P-orbit in . We consider some instances when P acts with a dense orbit on terms of the descending central series of . In particular, we show (in good characteristic) that a Borel subgroup B of a classical group acts on with a dense orbit for all l. Further we give some families of parabolic subgroups P such that contains a dense P-orbit for all l.

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