A new description of the Serre functor for perverse sheaves on $\mathbb{P}^n$

The constructible derived category of $\mathbb{P}^n$ is equivalent to the bounded derived category of the principal block of parabolic category $\mathcal O$ for $\mathfrak{sl}_n$, and to the bounded derived category of a certain special biserial algebra. In the latter two languages, the Serre functor can be explicitly described: as a concatenation of shuffling functors from the perspective of category $\mathcal O$ by results of Mazorchuk–Stroppel, and as the Nakayama functor from the perspective of finite-dimensional algebras by results of Happel. In this talk, I will explain a description of the Serre functor from the perspective of perverse sheaves. This is joint work with Lukas Bonfert.