Let $G$ be a compact Lie group and $a\in\mathfrak{g}^*$ (dual of Lie algebra of Lie group $G$). Then let $O_a$ be a coadjoint orbit. Then every coadjoint orbit is Kahler manifolds and also projective variety. How can we compute the Kodaira dimension of coadjoint orbit as projective variety? Is it $-\infty$