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arXiv · 1307.1322

Homological algebra for osp(1/2n)

Kevin Coulembier
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Abstract

We discuss several topics of homological algebra for the Lie superalgebra osp(1|2n). First we focus on Bott-Kostant cohomology, which yields classical results although the cohomology is not given by the kernel of the Kostant quabla operator. Based on this cohomology we can derive strong Bernstein-Gelfand-Gelfand resolutions for finite dimensional osp(1|2n)-modules. Then we state the Bott-Borel-Weil theorem which follows immediately from the Bott-Kostant cohomology by using the Peter-Weyl theorem for osp(1|2n). Finally we calculate the projective dimension of irreducible and Verma modules in the category O.

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Kevin Coulembier. 2013-07-22. Homological algebra for osp(1/2n). https://arxiv.org/abs/1307.1322

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