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- W2107257842 abstract "The notion of gluing of abelian categories was introduced in a paper by Kazhdan and Laumon in 1988 and studied further by 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 $mathcal{D}$ on the basic affine space $G/U$ (here $G$ is a semi-simple simply connected algebraic group over $mathbb{C}$ and $Usubset G$ is a maximal unipotent subgroup). We show that the category of $mathcal{D}$-modules is glued from $|W|$ copies of the category of $D$-modules on $G/U$ where $W$ is the Weyl group, and the Fourier transform is used to define the gluing data. As an application we prove that the algebra $mathcal{D}$ is Noetherian, and get some information on its homological properties. AMS 2000 Mathematics subject classification: Primary 13N10; 16S32; 17B10; 18C20" @default.
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- W2107257842 date "2002-10-01" @default.
- W2107257842 modified "2023-09-27" @default.
- W2107257842 title "GLUING OF ABELIAN CATEGORIES AND DIFFERENTIAL OPERATORS ON THE BASIC AFFINE SPACE" @default.
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- W2107257842 doi "https://doi.org/10.1017/s1474748002000154" @default.
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