The Beilinson-Bernstein correspondence for quantized enveloping algebras. (Q1779875)

The Beilinson-Bernstein correspondence provides the foundation of the applications of the theory of \(D\)-modules to the representation theory of semisimple Lie algebras. In the paper under review, the Beilinson-Bernstein correspondence for the quantized enveloping algebras is established which is comparable with the work by \textit{V. A. Lunts} and \textit{A. L. Rosenberg} [Sel. Math., New Ser. 3, No. 3, 335--359 (1997; Zbl 0937.16040)].