A classification of nilpotent orbits in infinitesimal symmetric spaces

JOURNAL OF ALGEBRA

卷:323

Article

Fox, Joseph A.

关键词: Algebraic groups;    Nilpotent orbits;    Good characteristic;    Involutions;    Associated cocharacters;   

DOI  :  10.1016/j.jalgebra.2009.12.022

来源: Elsevier

【 摘 要 】

Let G be a semisimple algebraic group defined over an algebraically closed field k whose characteristic is very good for G and not equal to 2. Suppose theta is an involution on G. We also denote the induced involution on g by theta. Let K = {g is an element of G: theta(g) = g} and let p be the - 1-eigenspace of theta in g. The adjoint action of G on g induces an action of K on p and on the variety N(p), which consists of the nilpotent elements in p. In this paper, we give a classification of the K-orbits in N(p). To do so, we use the theory of associated cocharacters developed by Pommerening. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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