习题 6, § 13

记号是no. 2.IV、型 $B_l$。 Show that, if $1\leq r\leq l-1$, the dimension of $E(\varpi_r)$ is $(^{2l+1}_r)$, and deduce another proof of the fact that $\bigwedge^r\sigma$ is a fundamental representation of highest weight $\varpi_r$.