Abstract
In this paper we prove a criterion for a parabolic subgroup P of a reductive algebraic group G to be of positive modality, i.e. to act with an infinite number of orbits on the unipotent radical. This condition is simply a lower bound on the length of the descending central series of the radical. We also show that in this situation we can always find a proper P-invariant linear subspace in the Lie algebra of the radical of P which admits an infinite number of P-orbits, unless P is maximal.
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This research was supported by ARC Grant # A69030627 (chief investigator: Prof. G. Lehrer).
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Röhrle, G. Parabolic subgroups of positive modality. Geom Dedicata 60, 163–186 (1996). https://doi.org/10.1007/BF00160621
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DOI: https://doi.org/10.1007/BF00160621