Tilting modules of affine quasi-hereditary algebras

Ryo Fujita

doi:10.1016/j.aim.2017.11.013

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arXiv · 1610.02621

Tilting modules of affine quasi-hereditary algebras

Ryo Fujita

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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 $GL_{n}$.

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Ryo Fujita. 2016-10-09. Tilting modules of affine quasi-hereditary algebras. https://doi.org/10.1016/j.aim.2017.11.013

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