Wall-Crossing functors and D-modules

Abstract

We study Translation functors and Wall-Crossing functors on infinite dimensional representations of a complex semisimple Lie algebra using D-modules. This functorial machinery is then used to prove the Endomorphism-theorem and the Structure-theorem, two important results established earlier by W. Soergel in a totally different way. Other applications to the category O of Bernstein-Gelfand-Gelfand are given, and some conjectural relationships between Koszul duality, Verdier duality and convolution functors are discussed. A geometric interpretation of tilting modules is given.

28pp., AMSTeX, added results on Tilting modules

Cited by in corpus (5)

• Shifted quantum affine algebras: integral forms in type $A$ (with appendices by Alexander Tsymbaliuk and Alex Weekes)
• Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture
• Sheaves on Triangulated Spaces and Koszul Duality
• Beilinson-Bernstein localization over the Harish-Chandra center
• Combinatorial Wall-Crossing and the Mullineux Involution