A classification of parabolic subgroups of classical groups with a finite number of orbits on the unipotent radical |
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Authors: | L Hille G Röhrle |
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Institution: | (1) Fakultät für Mathematik, TU Chemnitz, 09107 Chemnitz, Germany;(2) Fakultät für Mathematik, Universität Bielefeld, 33615 Bielefeld, Germany |
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Abstract: | LetG be a classical algebraic group defined over an algebraically closed field. We classify all instances when a parabolic subgroupP ofG acts on its unipotent radicalP
u
, or onp
u
, the Lie algebra ofP
u
, with only a finite number of orbits.The proof proceeds in two parts. First we obtain a reduction to the case of general linear groups. In a second step, a solution for these is achieved by studying the representation theory of a particular quiver with certain relations.Furthermore, for general linear groups we obtain a combinatorial formula for the number of orbits in the finite cases. |
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Keywords: | |
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