Identification of simple representations for affine q-Schur algebras

We define an explicit action of the quantum loop algebra Uq(glˆn) on the tensor space and show that these actions are compatible with the natural embedding Uq(glˆn)↪Uq(glˆn+1). As an application, we identify simple representations of affine q-Schur algebras S▵(n,r)C arising from simple polynomial representations of Uq(glˆn) (Frenkel and Mukhin, 2002) [11] with those arising from simple modules of the affine Hecke algebra H▵(r)C of type A (Rogawski, 1985) [26].