Homological algebra for osp(1/2n)
Representation Theory
2014-04-16 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1307.1322,
title = {Homological algebra for osp(1/2n)},
author = {Kevin Coulembier},
journal= {arXiv preprint arXiv:1307.1322},
year = {2014}
}