The orbit structure of Dynkin curves

Simon Goodwin, L Hille, G Röhrle

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 languageEnglish
Pages (from-to)439-451
Number of pages13
JournalMathematische Zeitschrift
Issue number2
Early online date21 Jun 2007
Publication statusPublished - 23 Jul 2007


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