  Let $A_n(K)$ be the Kostant form of $\mathfrak{U}(sl_n^+)$ and $\Gamma$ the
monoid generated by the positive roots of $sl_n$. For each $\lambda\in
\Lambda(n,r)$ we construct a functor $F_{\lambda}$ from the category of
finitely generated $\Gamma$-graded $A_n(K)$-modules to the category of finite
dimensional $S^+(n,r)$-modules, with the property that $F_{\lambda}$ maps
(minimal) projective resolutions of the one-dimensional $A_n(K)$-module $K_{A}$
to (minimal) projective resolutions of the simple $S^+(n,r)$-module
$K_{\lambda}$.
