Borel-Weil-Bott theory for classical Lie superalgebras

Category of Finite Dimensional Modules over an Orthosymplectic Lie Superalgebra: Small Rank Examples

“…However, one can give a geometric interpretation Borel-Weil-Bott like for Kac modules for gl(m, n), as the space of sections of a line bundle over the super flag variety. Hence, one can make the corresponding construction in the osp case ( [14]): now the cohomology is no longer concentrated in degree 0, and as is first mentioned in [16], we introduce the Euler characteristic which is a virtual module in the Grothendieck group K(F) of the category defined as the alternating sum of the cohomolgy groups: we will be more precise later.…”

Structure and representations on the quantum supergroup OSPq(2|2n)

“…For the classical Lie supergroups, the program of developing a Bott-Borel-Weil theory was extensively investigated by Penkov and co-workers. 22,25 Also, a quantum Borel-Weil theorem for GL q (m͉n) and OSP q (1͉2n) were established in Refs. 3 and 4.…”

Book Review: Lie superalgebras and enveloping algebras

“…Again the reader familiar with the positive characteristic case can see the analogy with Weyl modules for Chevalley groups. This approach is based on many important results in supergeometry obtained in the 1980s, in particular on the result of Penkov [19] that the Borel-Weil-Bott theorem holds for line bundles with typical weights. This approach was applied successfully for q(n) in [20] and to the orthosymplectic superalgebra in [13].…”