Asymptotic cone of semisimple orbits for symmetric pairs

Details Asymptotic cone of semisimple orbits for symmetric pairs Asymptotic cone of semisimple orbits for symmetric pairs

2010-12-15

arxiv.org/abs/1012.3219v1

Adv. Math. 226 (2011), no. 5, 4338--4351

Mathematics

Representation Theory

14 pages

Scientific paper

10.1016/j.aim.2010.12.004

Let G be a reductive algebraic group over the complex field and O_h be a closed adjoint orbit through a semisimple element h. By a result of Borho and Kraft (1979), it is known that the asymptotic cone of the orbit O_h is the closure of a Richardson nilpotent orbit corresponding to a parabolic subgroup whose Levi component is the centralizer Z_G(h) in G. In this paper, we prove an analogue on a semisimple orbit for a symmetric pair (G, K).

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