# Four examples of Beilinson–Bernstein localization

@article{Romanov2020FourEO,
title={Four examples of Beilinson–Bernstein
localization},
author={Anna Romanov},
journal={arXiv: Representation Theory},
year={2020}
}
• A. Romanov
• Published 4 February 2020
• Mathematics
• arXiv: Representation Theory
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…
1 Citations

## Figures from this paper

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• Mathematics
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