Symmetric spaces of hermitian type

AbstractLet M =G/H be a semisimple symmetric space,τ the corresponding involution and D =G/K the Riemannian symmetric space. Then we show that the followingare equivalent: M is of Hermitian type; τ induces a conjugation on D; thereexists an open regular H-invariant cone Ω in q =h[bottom] such that k ∩ Ω ≠ 0. We relate the spaces of Hermitian type to the regular and parahermitian symmetric spaces, analyze the fine structure of D under τ and construct an equivariant Cayley transform. We collect also some results on the classification of invariant cones in q. Finally we point out some applications in representations theory