$\mathcal{U}(\mathfrak{h})$-free modules and coherent families
Representation Theory
2017-07-11 v2
Abstract
We investigate the category of U(h)-free g-modules. Using a functor from this category to the category of coherent families, we show that U(h)-free modules only can exist when g is of type A or C. We then proceed to classify isomorphism classes of U(h)-free modules of rank 1 in type C, which includes an explicit construction of new simple sp(2n)-modules. Finally, we show how translation functors can be used to obtain simple U(h)-free modules of higher rank.
Cite
@article{arxiv.1501.03091,
title = {$\mathcal{U}(\mathfrak{h})$-free modules and coherent families},
author = {Jonathan Nilsson},
journal= {arXiv preprint arXiv:1501.03091},
year = {2017}
}
Comments
Updated, section 3.6 differs from the journal version. 14 pages