Wall-Crossing functors and D-modules

Details Wall-Crossing functors and D-modules Wall-Crossing functors and D-modules

1997-09-22

arxiv.org/abs/alg-geom/9709022v4

Mathematics

Algebraic Geometry

28pp., AMSTeX, added results on Tilting modules

Scientific paper

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.

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