On the derived category of IGr(3, 9)

We construct a minimal Lefschetz decomposition of the bounded derived category of the odd isotropic Grassmannian $\mathsf{I}\mathsf{G}\mathsf{r}(3,9)$. The exceptional objects are ${\mathsf{S}\mathsf{p}}_9$-equivariant vector bundles. This provides further evidence of the Kuznetsov-Smirnov version of Dubrovin conjecture.