Let $G$ be a compact Lie group and $\mathfrak{g}$ be its Lie algebra and $\mathfrak{g}^*$ be its dual , then I am looking for explicit formula for hermitian form on coadjoint orbit of $G$ on $\mathfrak{g}^*$.(note that $h=g-i\omega$ and for $\omega$ we have Kirilov symplectic 2-form )(maybe it be possible by Hodge star , but i couldn't find)

3more comments