Vector fields on osp2m|2n(C)- and πspn(C)-flag supermanifolds

The paper is devoted to a computation of the Lie superalgebras of holomorphic vector fields on isotropic flag supermanifolds of maximal type corresponding to the Lie superalgebras osp2m|2n(C) and πspn(C). The result is that under some restrictions on the flag type any holomorphic vector field is fundamental with respect to the natural action of the Lie superalgebras osp2m|2n(C) or πspn(C).