Abstract
The principal aim of this paper is to show that every maximal parabolic subgroup P of a classical reductive algebraic group G operates with a finite number of orbits on its unipotent radical. This is a consequence of the fact that each parabolic subgroup of a group of type A n whose unipotent radical is of nilpotent class at most two has this finiteness property.
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RÖhrle, G. Maximal Parabolic Subgroups in Classical Groups are of Modality Zero. Geometriae Dedicata 66, 51–64 (1997). https://doi.org/10.1023/A:1004941207559
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DOI: https://doi.org/10.1023/A:1004941207559