1997/09/22 by Alexander Beilinson, Victor Ginzburg, Beilinson, Alexander +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #alg-geom #math.AG #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.alg-geom/9709022
28pp., AMSTeX, added results on Tilting modules
arxiv created 1998/12/05 · arxiv updated 2009/11/30
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.