Grothendieck local cohomology and induced representations of Lie superalgebras (Q1318172)

Let \({\mathfrak g}\) be a Lie superalgebra and let \({\mathfrak h}\) be a finite codimensional Lie subsuperalgebra of \({\mathfrak g}\). We give a realization of an induced representation of \({\mathfrak g}\) from a \({\mathfrak h}\)-module in terms of Grothendieck local cohomology. This generalizes a result proved by \textit{W. Borho} and \textit{J. L. Brylinski} [Invent. Math. 69, 437-476 (1982; Zbl 0504.22015)] in the case of finite dimensional Lie algebras. As a corollary of our results, we give a new proof of a duality property in coinduced representations of Lie superalgebras [\textit{M. Duflo}, Invent. Math. 67, 385-393 (1982; Zbl 0501.17006) and the author (Thesis, Paris 7)]. All our statements hold over a field of characteristic 0.