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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157770Let $A_n(K)$ be the Kostant form of $\mathfrak{U}(sl_n^+)$ and $Γ$ the monoid generated by the positive roots of $sl_n$. For each $λ\in Λ(n,r)$ we construct a functor $F_λ$ from the category of finitely generated $Γ$-graded $A_n(K)$-modules to the category of finite dimensional $S^+(n,r)$-modules, with the property that $F_λ$ 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 $K_λ$.38 pagesRepresentation TheoryRings and Algebras16G99; 16E05; 16E60The Kostant form of $\mathfrak{U}(sl_n^+)$ and the Borel subalgebra of the Schur algebra S(n,r)text