>>If $P(V^w_\lambda)$ denotes the set of weights which appear in the Demazure module, I can consider the convex hull in $X^* \otimes_\mathbb{Z} \mathbb{R}$. The extremal vertices of the resulting polytope will be $w'(\lambda)$ for $w' \leq w$ via an argument of Bernstein, Gelfand and Gelfand.<< I am not sure if it is appropriate to pose this question here (apologies if it isn't), but would you happen to know the exact reference to Bernstein-Gelfand-Gelfand's argument which proves the above statement ?