The orbit structure of Dynkin curves
| dc.creator | Goodwin, Simon M. | |
| dc.creator | Hille, Lutz | |
| dc.creator | Roehrle, Gerhard | |
| dc.date | 2006-08-23 | |
| dc.date | 2007-01-17 | |
| dc.date.accessioned | 2026-07-07T07:41:16Z | |
| dc.date.available | 2026-07-07T07:41:16Z | |
| dc.description | Let G be a simple algebraic group over an algebraically closed field k; assume that Char k is zero or good for G. Let \cB be the variety of Borel subgroups of G and let e in Lie G be nilpotent. There is a natural action of the centralizer C_G(e) of e in G on the Springer fibre \cB_e = {B' in \cB | e in Lie B'} associated to e. In this paper we consider the case, where e lies in the subregular nilpotent orbit; in this case \cB_e is a Dynkin curve. We give a complete description of the C_G(e)-orbits in \cB_e. In particular, we classify the irreducible components of \cB_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. | |
| dc.description | 12 pages, to appear in Math Z | |
| dc.identifier | https://arxiv.org/abs/math/0608579 | |
| dc.identifier | http://arxiv.org/abs/math/0608579 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122045 | |
| dc.subject | Group Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 20G15 | |
| dc.title | The orbit structure of Dynkin curves | |
| dc.type | text |