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Given a Lie group $G$, it acts smoothly on the dual $\mathfrak g^*$ of its Lie algebra $\mathfrak g$ by the coadjoint action. The orbits of that action are called coadjoint orbits.

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Branching problem of representation of Lie groups and orbit method

Branching problem asks how a restriction of an irreducible representation of $G$ to a subgroup $H$ decomposes. In case of (real) Lie groups, after labeling irreducible representations via highest weig …
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