On the bounded derived category of $\mathsf{I}\mathsf{G}\mathsf{r}(3,7)$

We construct a mininal Lefschetz decomposition of the bounded derived category of coherent sheaves on the isotropic Grassmannian $\mathsf{I}\mathsf{G}\mathsf{r}(3,7)$. Moreover, we show that $\mathsf{I}\mathsf{G}\mathsf{r}(3,7)$ admits a full exceptional collection consisting of equivariant vector bundles.