A classification of nilpotent orbits in infinitesimal symmetric spaces

作者：Fox Joseph A^*

来源：Journal of Algebra, 2010, 323(5): 1358-1368.

DOI：10.1016/j.jalgebra.2009.12.022

• Algebraic groups
• Nilpotent orbits
• Good characteristic
• Involutions
• Associated cocharacters

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.

• 出版日期2010-3-1