Root involutions, real forms and diagrams

We study the correspondence between equivalence classes of pairs consisting of real semisimple Lie algebras and their Cartan subalgebras and involutions of the corresponding root system. This can be graphically described by introducing \emph{$S\text{\hspace{0.17em}⁣}${-} and $\mathrm{\Sigma }$-diagrams}, generalizing those of Satake and Vogan.