Let $G$ be a compact Lie group and $\mathfrak{g}$ the corresponding Lie algebra. Now, $G$ also acts on $\mathfrak{g}^*$, the dual of the Lie algebra, by the coadjoint-action.
My question now is: are the orbits of the $G$-action in $\mathfrak{g}^*$ real analytic? And if so, why and where could I read about it?
Edit: From the comment we know, that $G$ acts linearly on $\mathfrak{g}^*$ and $G$ can be endowed with some real analytic structure. But how does that imply, that the $G$-orbits are real analytic?