The Kostant form of $\mathfrak{U}(s{l}_n^{+})$ and the Borel subalgebra of the Schur algebra S(n,r)

Abstract

Let $A_n(K)$ be the Kostant form of $\mathfrak{U}(s{l}_n^{+})$ and $\Gamma$ the monoid generated by the positive roots of $s{l}_n$. 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 $K_{\lambda }$.

38 pages