On the complement of the Richardson orbit

Details On the complement of the Richardson orbit On the complement of the Richardson orbit

2010-03-26

arxiv.org/abs/1003.5234v2

Mathematics

Representation Theory

15 pages

Scientific paper

10.1007/s00209-011-0920-9

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 $\ge 6$. In this paper, we describe the irreducible components of the complement. In particular, we show that there are at most $t-1$ irreducible components.

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