University of Sydney Algebra Seminar

Kevin Coulembier; (University of Sydney)

Friday 11 Sep, 12-1pm, Place: Carslaw 375

Ringel duality and derived equivalences for BGG category O

Category O and its parabolic generalisations are amongst the original motivating examples for the concept of quasi-hereditary algebras and highest weight categories. We determine the Ringel duals of arbitrary blocks in parabolic category O, completing previous results by Soergel, Mazorchuk and Stroppel. Furthermore, we use generalisations of the Ringel duality functor to obtain large classes of derived equivalences between blocks in (parabolic) category O. This extends and provides an algebraic proof for certain derived equivalences observed by Khovanov. For type A, our results lead to a complete classification of equivalences between blocks of original category O.