Tilting modules of affine quasi-hereditary algebras

We discuss tilting modules of affine quasi-hereditary algebras. We present an existence theorem of indecomposable tilting modules when the algebra has a large center and use it to deduce a criterion for an exact functor between two affine highest weight categories to give an equivalence. As an application, we prove that the Arakawa-Suzuki functor (Arakawa-Suzuki, 1998) gives a fully faithful embedding of a block of the deformed BGG category of glm into the module category of a suitable completion of degenerate affine Hecke algebra of GLn.