  We define a higher level version of the affine Hecke algebra and prove that,
after completion, this algebra is isomorphic to a completion of Webster's
tensor product algebra of type A. We then introduce a higher level version of
the affine Schur algebra and establish, again after completion, an isomorphism
with the quiver Schur algebra. An important observation is that the higher
level affine Schur algebra surjects to the Dipper-James-Mathas cyclotomic
q-Schur algebra. Moreover, we give nice diagrammatic presentations for all the
algebras introduced in this paper.

Representation Theory;Rings and Algebras