A classification of nilpotent orbits in infinitesimal symmetric spaces. (Q965158)

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 \(G\). The induced involution on \(\mathfrak g\) is also denoted by \(\theta\). Let \(K=\{g\in G:\theta(g)=g\}\) and let \(\mathfrak p\) be the \(-1\)-eigenspace of \(\theta\) in \(\mathfrak g\). The adjoint action of \(G\) on \(\mathfrak g\) induces an action of \(K\) on \(\mathfrak p\) and on the variety \(\mathcal N(\mathfrak p)\), which consists of the nilpotent elements in \(\mathfrak p\). A classification of the \(K\)-orbits in \(\mathcal N(\mathfrak p)\) is given. The theory of associated cocharacters developed by Pommerening is used.