Prehomogeneous Spaces for Parabolic Group Actions in Classical Groups
نویسندگان
چکیده
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 pu of Pu. Richardson’s dense orbit theorem says that there is a dense P -orbit in pu. We consider some instances when P acts with a dense orbit on terms p u of the descending central series of pu. In particular, we show (in good characteristic) that a Borel subgroup B of a classical group acts on b u with a dense orbit for all l. Further we give some families of parabolic subgroups P such that p u contains a dense P -orbit for all l.
منابع مشابه
Maximal prehomogeneous subspaces on classical groups
Suppose $G$ is a split connected reductive orthogonal or symplectic group over an infinite field $F,$ $P=MN$ is a maximal parabolic subgroup of $G,$ $frak{n}$ is the Lie algebra of the unipotent radical $N.$ Under the adjoint action of its stabilizer in $M,$ every maximal prehomogeneous subspaces of $frak{n}$ is determined.
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