Gluing of abelian categories and differential operators on the basic affine space

Roman Bezrukavnikov, Alexander Braverman, Leonid Positselskii

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


The notion of gluing of abelian categories was introduced in a paper by Kazhdan and Laumon in 1988 and studied furtherby Polishchuk. We observe that this notion is a particular case of a general categorical construction. We then apply this general notion to the study of the ring of global differential operators on the basic affinespace (here is a semi-simple simply connected algebraic group over and is a maximalunipotent subgroup). We show that the category of -modules is glued from copies of the category of D-modules on G/U whereW is the Weyl group, and the Fourier transform is used to define the gluing data. As an application we prove that thealgebra \mathcal{D} is Noetherian, and get some information on its homological properties.

Original languageEnglish
Pages (from-to)543-557
Number of pages15
JournalJournal of the Institute of Mathematics of Jussieu
Issue number4
Publication statusPublished - Oct 2002
Externally publishedYes


  • gluing of categories
  • rings of differential operators
  • semisimple Lie algebras


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