The action of the maximal compact subgroups of semisimple groups

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Let $S$ be a semisimple complex algebraic group. Let $K$ be a maximal compact subgroup of $S$. Consider the transitive action of $S$ on the space $X$ such that $K$-orbits are compact in $X$. Dose this imply the compactness of $X$?




algebraic-geometry lie-groups algebraic-groups




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    Let $S$ be a semisimple complex algebraic group. Let $K$ be a maximal compact subgroup of $S$. Consider the transitive action of $S$ on the space $X$ such that $K$-orbits are compact in $X$. Dose this imply the compactness of $X$?




    algebraic-geometry lie-groups algebraic-groups




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      Let $S$ be a semisimple complex algebraic group. Let $K$ be a maximal compact subgroup of $S$. Consider the transitive action of $S$ on the space $X$ such that $K$-orbits are compact in $X$. Dose this imply the compactness of $X$?




      algebraic-geometry lie-groups algebraic-groups




      share|cite|improve this question











      Let $S$ be a semisimple complex algebraic group. Let $K$ be a maximal compact subgroup of $S$. Consider the transitive action of $S$ on the space $X$ such that $K$-orbits are compact in $X$. Dose this imply the compactness of $X$?





      algebraic-geometry lie-groups algebraic-groups





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Aug 4 at 2:46









      Ronald

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