2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147226We 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 modulesAlgebraic GeometryQuantum Algebratext