Abstract
Let G be a simple algebraic group over an algebraically closed field k; assume that char k is zero or good for G. Let B be the variety of Borel subgroups of G and let e is an element of Lie G be nilpotent. There is a natural action of the centralizer CG( e) of e in G on the Springer fibre B-e = {B' is an element of B vertical bar e is an element of Lie B'} associated to e. In this paper we consider the case, where e lies in the subregular nilpotent orbit; in this case B-e is a Dynkin curve. We give a complete description of the CG(e)-orbits in B-e. In particular, we classify the irreducible components of B-e on which C-G(e) acts with finitely many orbits. In an application we obtain a classification of all subregular orbital varieties admitting a finite number of B-orbits for B a fixed Borel subgroup of G.
Original language | English |
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Pages (from-to) | 439-451 |
Number of pages | 13 |
Journal | Mathematische Zeitschrift |
Volume | 257 |
Issue number | 2 |
Early online date | 21 Jun 2007 |
DOIs | |
Publication status | Published - 23 Jul 2007 |