Vector fields on \(\Pi \)-symmetric flag supermanifolds (Q332606)

From the text: The main result of this paper is the computation of the Lie superalgebras of holomorphic vector fields on the complex \(\Pi \)-symmetric flag supermanifolds, introduced by Yu. I. Manin. The author proves that with one exception any vector field is fundamental with respect to the natural action of the Lie superalgebra \(\mathfrak {q}_n(\mathbb {C})\). The main result of this paper was announced in [Russ. Math. Surv. 63, No. 2, 394--396 (2008); translation from Usp. Mat. Nauk 63, No. 2, 163--164 (2008; Zbl 1209.17020)] and the idea of proof was given in [Vestn. Tver. Gos. Univ., Ser. Prikl. Mat. 7, 117--127 (2007; \url{http://elibrary.ru/item.asp?id=11658318})]. The goal of this note is to give a detailed proof. She also describes the connected component of the automorphism supergroup of this supermanifold.