##  [Beilinson–Bernstein Localization](/beilinson-bernstein-localization) 

  ##  [Beilinson–Bernstein Localization](https://algebra.quantumdictionary.io/beilinson-bernstein-localization-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An equivalence between certain categories of representations of a complex semisimple Lie algebra (notably blocks of category O with fixed central character) and categories of (twisted) D-modules on the flag variety, realizing algebraic representation problems geometrically on the flag manifold.