Spherical nilpotent orbits in positive characteristic

Russell Fowler and Gerhard Röhrle

Vol. 237 (2008), No. 2, 241–286

DOI: 10.2140/pjm.2008.237.241

Abstract

Let G be a connected reductive linear algebraic group defined over an algebraically closed field of characteristic p. Assume that p is good for G. In this note we classify all the spherical nilpotent G-orbits in the Lie algebra of G. The classification is the same as in the characteristic zero case obtained by D. I. Panyushev [1994]: for e a nilpotent element in the Lie algebra of G, the G-orbit G ⋅ e is spherical if and only if the height of e is at most 3.

Keywords

spherical orbit, nilpotent orbit, associated cocharacter

Mathematical Subject Classification 2000

Primary: 20G15, 14L30

Secondary: 17B50

Milestones

Received: 7 December 2007

Revised: 27 May 2008

Accepted: 30 May 2008

Published: 1 October 2008