Abstract
Let 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.
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