Geodesic
Borel--Weil--Bott theory for classical Lie supergroups
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 32 (1988), pp. 71-124

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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 $G^0$-sheaves on $G^0/B$, where $G^0$ is the connected component of the identity in a classical complex Lie supergroup and $B\hookrightarrow G^0$ an arbitrary Borel subsupergroup. Also presented are some simple known results concerning the cohomology of irreducible $G^0$-sheaves on $G^0/P$ for a parabolic subsupergroup $P$. 
@article{INTD_1988_32_a2,
     author = {I. B. Penkov},
     title = {Borel--Weil--Bott theory for classical {Lie} supergroups},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {71--124},
     publisher = {mathdoc},
     volume = {32},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTD_1988_32_a2/}
}
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I. B. Penkov. Borel--Weil--Bott theory for classical Lie supergroups. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 32 (1988), pp. 71-124. http://geodesic.mathdoc.fr/item/INTD_1988_32_a2/