Borel-Weil-Bott theorem for algebraic supergroups and weak BGG reciprocity

We will review some results about superanalogue of Borel-Weil-Bott theorem, explain the role of Weyl groupoid and prove a weak version of BGG reciprocity. Then we illustrate how BGG reciprocity can be used for computing the Cartan matrix of the category of finite dimensional representations of the nontivial central extension of the periplectic supergroup P(4).