On sheaf cohomology for supergroups arising from simple classical Lie superalgebras

2022/03/05 by Galban, David M., Nakano, Daniel K.
#17B10 #17B56 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2203.02775

Abstract

In this paper the authors study the behavior of the sheaf cohomology functors R^\bulletind_B^G(-) where G is an algebraic group scheme corresponding to a simple classical Lie superalgebra and B is a BBW parabolic subgroup as defined by D. Grantcharov, N. Grantcharov, Nakano and Wu. We provide a systematic treatment that allows us to study the behavior of these cohomology groups R^\bulletind_B^GL_{\mathfrak f}(λ) where L_{\mathfrak f}(λ) is an irreducible representation for the detecting subalgebra \mathfrak f. In particular, we prove an analog of Kempf's vanishing theorem and the Bott-Borel-Weil theorem for large weights.

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