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8 votes
1 answer
461 views

Existence of at least one compact orbit on the sphere

Good morning, I've came across this question during my researches. It seems apparently very simple, however I Googled a bit and I couldn't find the answer I was looking for. The question is as ...
1 vote
1 answer
308 views

Holomorphic representations of complex reductive Lie groups and the boundary of orbits (Reference request)

I have difficulties finding an appropriate reference for the following question (which I hope that it to be true). Let $U$ be a compact Lie group, $G:=U^{\mathbb{C}}$ its complexification and $\tau: U^...