On the complement of the Richardson orbit |
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Authors: | Karin Baur Lutz Hille |
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Institution: | 1. Department of Mathematics, ETH Zürich, R?mistrasse 101, 8092, Zurich, Switzerland 2. Mathematisches Institut, Fachbereich Mathematik und Informatik der Universit?t Münster, Einsteinstrasse 62, 48149, Münster, Germany
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Abstract: | We consider parabolic subgroups of a general linear group over an algebraically closed field k whose Levi part has exactly t factors. By a classical theorem of Richardson, the nilradical of a parabolic subgroup P has an open dense P-orbit. In the complement to this dense orbit, there are infinitely many orbits as soon as the number t of factors in the Levi part is ≥6. In this paper, we describe the irreducible components of the complement. In particular, we show that there are at most t ? 1 irreducible components. We are also able to determine their codimensions. |
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