Borel-Weil-Bott theory for classical Lie superalgebras

The paper is devoted to a systematic construction of the elements of Borel-Weil-Bott theory in the supercase. The main result is a presentation of the cohomology of typical irreducible G-sheaves on G/B, where G is the connected component of the identity in a classical complex Lie supergroup and B G an arbitrary Borel subsupergroup. Also presented are some simple known results concerning the cohomology of irreducible G-sheaves on G/P for a parabolic subsupergroup P.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 32, pp. 71–124, 1988.