Compactification of symmetric spaces

Let G be a connected real semisimple Lie group with finite center and θ be a Cartan involution of G. Suppose that K is the maximal compact subgroup of G corresponding to the Cartan involution θ. The coset space X = G/K is then a Riemannian symmetric space. Denote by g the Lie algebra of G and g = k + p the Cartan decomposition of g into eigenspaces of θ. Let a be a maximal abelian subspace in p and Σ be the corresponding restricted root system.

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