Affine Quasi-Heredity of Affine Schur Algebras

In this paper we prove that the affine Schur algebra (widehat {S}(n,r)) is affine quasi-hereditary. This result is then used to show that the centralizer subquotient algebras of (widehat {S}(n,r)) are Laurent polynomial algebras. Moreover, we give a parameter set of simple (widehat {S}(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.