Four examples of Beilinson–Bernstein localization

  title={Four examples of Beilinson–Bernstein
  author={Anna Romanov},
  journal={arXiv: Representation Theory},
  • 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… 
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