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From the representation category of a Lie group and the representation on a homogeneous spac...
I understand it for finite groups now, and I suspect that it's similar for semisimple Lie groups.
These statements are equivalent, and true for finite groups:
The adjunction $\operatorname{Res} \da …
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From the representation category of a Lie group and the representation on a homogeneous spac...
Given a Lie group $G$ and a transitive action $- \triangleright - : G \times X \to X$ on a homogeneous space, we can recover the stabiliser subgroup $H_x$ of a point $x \in X$. It is the subgroup of $ …