A classification of nilpotent orbits in infinitesimal symmetric spaces

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 θ is an involution on G. We also denote the induced involution on g by θ. Let K = {g ∈ G : θ(g) = g} and let p be the −1-eigenspace of θ 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.