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arXiv · 1501.03091

$\mathcal{U}(\mathfrak{h})$-free modules and coherent families

Jonathan Nilsson
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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.

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BibTeXRIS

Jonathan Nilsson. 2015-01-13. $\mathcal{U}(\mathfrak{h})$-free modules and coherent families. https://doi.org/10.1016/j.jpaa.2015.09.013

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