Exercise 2, § 6

Let $\mu$ be a weight of $Z(\lambda )$ (resp. $E(\lambda )$). Show that there exists a sequence of weights $\mu_0, . . . , \mu_n$ of $Z(\lambda )$ (resp. of $E(\lambda )$) such that $\mu_0=\lambda , \mu_n=\mu$, and $\mu_{i-1}-\mu_i\in B$ for $1\leq i\leq n$.