David Galban: Cohomology and Representation Theory for Lie Superalgebras

This talk will consist of two parts. In the first, I will describe the cohomology groups for the subalgebra 𝔫⁺ relative to the BBW parabolic subalgebras constructed by D. Grantcharov, N. Grantcharov, Nakano and Wu, essentially with these calculations essentially providing the first steps towards an analogue of Kostant’s theorem for Lie superalgebras. In the second part, based on joint work with Nakano, I will analyze the sheaf cohomology groups R^I ind_B^G L_𝔣(λ), where L_𝔣(λ) is an irreducible representation for the detecting subalgebra 𝔣, providing analogues for the BBW theorem and Kempf’s vanishing theorem for sufficiently large λ.

This video is part of the University of Georgia‘s Algebra seminar.