Some results on Semisimple Symmetric Spaces and Invariant Differential Operators

Trần Đạo Dõng

DOI: http://dx.doi.org/10.26459/jns.v116i2.3762

Abstract


Let X = G/H be a semisimple symmetric space of non-compact style. Our purpose is to construct a compact real analytic manifold in which the semisimple symmetric space X = G/H is realized as an open subset and that $G$ acts analytically on it. By the Cartan decomposition G = KAH, we must compacify the vectorial part A.$ In [6], by using the action of the Weyl group, we constructed a compact real analytic manifold in which the semisimple symmetric space G/H is realized as an open subset and that G acts analytically on it.Our construction is a motivation of the Oshima's construction and it is similar to those in N. Shimeno, J. Sekiguchi for semismple symmetric spaces.In this note, first we will inllustrate the construction via the case of SL (n, R)/SO_e (1, n-1) and then show that the system of invariant differential operators on X = G/H extends analytically on the corresponding compactification.