Quantum flag varieties, equivariant quantum D-modules and localization of quantum groups

Journal article

Let $\Oq(G)$ be the algebra of quantized functions on an algebraic group $G$ and $\Oq(B)$ its quotient algebra corresponding to a Borel subgroup $B$ of $G$. We define the category of sheaves on the "quantum flag variety of $G$" to be the $\Oq(B)$-equivariant $\Oq(G)$-modules and proves that this is a proj-category. We construct a category of equivariant quantum $\mathcal{D}$-modules on this quantized flag variety and prove the Beilinson-Bernsteins localization theorem for this category in the case when $q$ is not a root of unity.

Authors: Backelin, E; Kremnizer, K

• Publication status: Published
• Journal: ADVANCES IN MATHEMATICS
• Volume: 203
• Issue: 2
• Pages: 408-429
• Publication date: 2004-01-11
• DOI: 10.1016/j.aim.2005.04.012
• EISSN: 1090-2082
• ISSN: 0001-8708
• Language: English
• Keywords: math.RT; math.QA