Homogeneous Spaces of Compact Connected Lie Groups Which Admit Nontrivial Invariant Algebras

In 1965 Wolf [10] and Gangolli [1] proved that compact semisimple groups are distinguished in the class of all compact connected Lie groups by the following property: every uniformly closed function algebra which is invariant with respect to left and right translations is also invariant with respect to the complex conjugation.In this article we extend this result to the class of homogeneous spaces of compact connected Lie groups with connected stable subgroups: a homogeneous space admits only self-conjugated invariant function algebras if and only if the isotropy representation has no nonzero fixed vectors.