Tilting modules of affine quasi-hereditary algebras

Abstract

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, J. of Alg. 209 (1998)] gives a fully faithful embedding of a block of the deformed BGG category of ${\mathfrak{gl}}_m$ into the module category of a suitable completion of degenerate affine Hecke algebra of $G{L}_n$.

25 pages, v2: minor modifications

References in corpus (2)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Affine highest weight categories and affine quasihereditary algebras

Cited by in corpus (4)

• Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types
• Representation theory of geometric extension algebras
• Equivalence between module categories over quiver Hecke algebras and Hernandez-Leclerc's categories in general types
• Strands algebras and the affine highest weight property for equivariant hypertoric categories