A compact imbedding of Riemannian Symmetric Spaces

SUMMARY

Let G be a connected real semisimple Lie group with finite center and ? be a Cartan involution of G. Suppose that K is the maximal compact subgroup of G corresponding to the Cartan involution ?. The coset space X = G/K is then a Riemannian symmetric space. In this paper, by choosing the reduced root system S0 = {a ? S | 2a /? S; a 2 ?/ S} insteads of the restricted root system S and using the action of the Weyl group, firstly we construct a compact real analytic manifold Xb 0 in which the Riemannian symmetric space G/K is realized as an open subset and that G acts analytically on it, then we consider the real analytic structure of Xb 0 induced from the real analytic srtucture of AbIR, the compactification of the corresponding vectorial part.