On the Complement of the Richardson Orbit

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Date
2010-03-13MFO Scientific Program
Research in Pairs 2009Series
Oberwolfach Preprints;2010,09Author
Baur, Karin
Hille, Lutz
Metadata
Show full item recordOWP-2010-09
Abstract
We consider parabolic subgroups of a general algebraic 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 $\geq 6$. 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.