Vector fields on $\mathrm{\Pi }$-symmetric flag supermanifolds

The main result of this paper is the computation of the Lie superalgebras of holomorphic vector fields on the complex $\mathrm{\Pi }$-symmetric flag supermanifolds, introduced by Yu.I.~Manin. We prove that with one exception any vector field is fundamental with respect to the natural action of the Lie superalgebra ${\mathfrak{q}}_n(\mathbb{C})$.