A Compact Imbedding of Semisimple Symmetric Spaces

J. Math. Sci. Univ. Tokyo
Vol. 3 (1996), No. 3, Page 551--569.

Shimeno, Nobukazu
A Compact Imbedding of Semisimple Symmetric Spaces
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Abstract:
A realization of a $\ep$-family of semisimple symmetric spaces $\{G/H_\ep\}$ in a compact real analytic manifold $\X$ is constructed. The realization $\X$ has the following properties: a) The action of $G$ on $\X$ is real analytic; b) There exist open $G$-orbits that are isomorphic to $G/H_\ep$ for each signature of roots $\ep$; c) The system $\Cal M_λ$ of invariant differential equations on $G/H_\ep$ extends analytically on $\X$ and has regular singularities in the weak sense along the boundaries.

Mathematics Subject Classification (1991): Primary 53C35; Secondary 22E46
Mathematical Reviews Number: MR1432109

Received: 1995-08-28