Serre functor and $\mathbb{P}$-objects for perverse sheaves on ${\mathbb{P}}^n$

We show that the inverse Serre functor for the constructible derived category ${\mathbf{D}}_{\mathrm{c}}^{\mathrm{b}}({\mathbb{P}}^n)$ is given by the $\mathbb{P}$-twist at the simple perverse sheaf corresponding to the open stratum. Moreover, we show that all indecomposable perverse sheaves on ${\mathbb{P}}^n$ are $\mathbb{P}$-like objects, and explicitly construct morphisms spanning their total endomorphism spaces.