Spherical Nilpotent Orbits in Positive Characteristic

Details Spherical Nilpotent Orbits in Positive Characteristic Spherical Nilpotent Orbits in Positive Characteristic

2007-08-07

arxiv.org/abs/0708.0923v3

Mathematics

Group Theory

35 pages to appear in Pacific J. Math

Scientific paper

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 in 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.

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