English

On the complement of the Richardson orbit

Representation Theory 2015-03-13 v2

Abstract

We consider parabolic subgroups of a general algebraic group over an algebraically closed field kk whose Levi part has exactly tt factors. By a classical theorem of Richardson, the nilradical of a parabolic subgroup PP has an open dense PP-orbit. In the complement to this dense orbit, there are infinitely many orbits as soon as the number tt of factors in the Levi part is 6\ge 6. In this paper, we describe the irreducible components of the complement. In particular, we show that there are at most t1t-1 irreducible components.

Keywords

Cite

@article{arxiv.1003.5234,
  title  = {On the complement of the Richardson orbit},
  author = {Karin Baur and Lutz Hille},
  journal= {arXiv preprint arXiv:1003.5234},
  year   = {2015}
}

Comments

15 pages

R2 v1 2026-06-21T15:03:16.348Z