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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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Interesting properties of "coadjoint" orbits inside $V\in \operatorname{Rep}G$

Generally they can be classified when the action of $G$ on $V$ is visible, which by definition means there are finitely many orbits in the nullcone. Irreducible visible pairs $(G, V)$ were classified …
Joshua Grochow's user avatar