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

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

2008-03-31

arxiv.org/abs/0803.4382v1

Mathematics

Representation Theory

38 pages

Scientific paper

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 $K_{\lambda}$.

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