# Four examples of Beilinson–Bernstein localization

@article{Romanov2020FourEO, title={Four examples of Beilinson–Bernstein localization}, author={Anna Romanov}, journal={arXiv: Representation Theory}, year={2020} }

Let $\mathfrak{g}$ be a complex semisimple Lie algebra. The Beilinson-Bernstein localization theorem establishes an equivalence of the category of $\mathfrak{g}$-modules of a fixed infinitesimal character and a category of modules over a twisted sheaf of differential operators on the flag variety of $\mathfrak{g}$. In this expository paper, we give four detailed examples of this theorem when $\mathfrak{g}=\mathfrak{sl}(2,\mathbb{C})$. Specifically, we describe the $\mathcal{D}$-modules…

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An investigation into Lie algebra representations obtained from regular holonomic D-modules

- Mathematics
- 2021

Beilinson–Bernstein localisation [BB81] relates representations of a Lie algebra g to certain D-modules on the flag variety of g. In [Rom21], examples of sl2-representations which correspond to…

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