The orbit structure of Dynkin curves

Goodwin, Simon, Hille, Lutz and Roehrle, Gerhard (2006) The orbit structure of Dynkin curves. Mathematische Zeitschrift. (In Press)

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 lete in Lie G be nilpotent. There is a natural action of the centralizer C_G(e) of e in G on the Springer fibre \B_e 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 C_G(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.

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