ar X iv : a lg - g eo m / 9 70 90 22 v 4 5 D ec 1 99 8 WALL - CROSSING FUNCTORS AND D - MODULES
نویسندگان
چکیده
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-GelfandGelfand 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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We study Translation functors and Wall-Crossing functors on inn-nite 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 were established earlier by W. Soergel in a totally diierent way. Other applications to the category O of Bernstein-Gelfand-G...
متن کاملar X iv : m at h . D G / 0 30 62 35 v 2 8 N ov 2 00 6 GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD THEORY
We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16] and [19] by a certain fractional power of the abelian theory first considered in [13] and further studied in [2].
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