Is it true that each irreducible sl(2,$\mathbb{C}$)-module, $P(\lambda,\mu)$ with $\lambda \in \mathbb{Z}$ appears as the harish chandra module of some $(\pi_{\chi},V_{\chi})$ And given $\lambda\in\mathbb{Z}$ and $\mu\in\mathbb{C}$ such that neither of $\lambda\pm\sqrt{\mu+1}$ is an odd integer what is $\chi$
also any good references on this material? I'v only seen a cursory introduction in some course notes but can't find any good book on this.