On the affine Schur algebra of type A II

By studying certain kind of centralizer algebras of the affine Schur algebra $\widetilde{S}(n,r)$ we show that $\widetilde{S}(n,r)$ is Noetherian and we determine its center. Assuming $n\geq r$, we show that $\widetilde{S}(n+1,r)$ is Morita equivalent to $\widetilde{S}(n,r)$, and the Schur functor is an equivalence under certain conditions.