Three perspectives on a certain Serre functor

The constructible derived category of P^n is equivalent to the bounded derived category of the principal block of parabolic category O for sl_n, and also to the bounded derived category of a certain special biserial algebra. In both of these languages, the Serre functor can be explicitly described: from the perspective of category O, results of Mazorchuk--Stroppel describe it as a concatenation of shuffling functors, and from the perspective of finite-dimensional algebras, results of Happel describe it as the Nakayama functor. In this talk, I will explain a description of the Serre functor from the perspective of perverse sheaves. This is joint work in progress with Alessio Cipriani.

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