Unitary Branching for $\mathfrak{sl}(m\vert n), \mathfrak{osp}(m\vert 2n)$ and $F(4)$

We determine the branching of irreducible unitary representations of the basic classical Lie superalgebras $\mathfrak{sl}(m|n)$, $\mathfrak{osp}(m|2n)$, and $F(4)$ under restriction to their even subalgebras. The proof combines Dirac inequalities for the Huang-Pandžić-Dirac operator $\operatorname{D