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- W2137348712 abstract "Let G be a reductive linear algebraic group, P a parabolic subgroup of G and P u its unipotent radical. We consider the adjoint action of P on the Lie algebra u of P u . Each higher term u (l) of the descending central series of u is stable under this action. For classical G all instances when P acts on u (l) with a finite number of orbits were determined in [9], [10], [3] and [4]. In this note we extend these results to groups of type F 4 and E 6 . Moreover, when P acts on u (l) with an infinite number of orbits, we determine whether P still acts with a dense orbit. For G of type E 7 and E 8 we investigate only the case of a Borel subgroup. We present a complete classification of all instances when u (l) is a prehomogeneous space for a Borel subgroup B of a reductive algebraic group for any l ≥ 0." @default.
- W2137348712 created "2016-06-24" @default.
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- W2137348712 date "2004-06-01" @default.
- W2137348712 modified "2023-09-24" @default.
- W2137348712 title "Finite orbit modules for parabolic subgroups of exceptional groups" @default.
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- W2137348712 doi "https://doi.org/10.1016/s0019-3577(04)90014-6" @default.
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