Hello,

Could anyone give a reference or proof for the following fact (which is, probably, not very difficult):

We work in category O for a semisimple complex Lie algebra. $M_{\chi}$ denotes the Verma module with shifted highest weight $\chi$.

Fact: Let $\chi$ be dominant, $\lambda$ be such that $\chi - \lambda$ is integral. Then there exists a finite dimensional module $E$ and a surjection $E \otimes M_{\chi} \to M_{\lambda}$.

It seems that one should first "move" from $\chi$ to a weight in the same Weyl orbit as $\lambda$, and then...

Thanks, Sasha