In this paper we prove that the affine Schur algebra (S) over cap (n, r) is affine quasi-hereditary. This result is then used to show that the centralizer subquotient algebras of (S) over cap (n, r) are Laurent polynomial algebras. Moreover, we give a parameter set of simple (S) over cap (n, r)-modules and identify this parameter set with that given in [7]. In the Appendix, the affine quasi-heredity of affine quantum Schur algebras is studied.
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