Tilting modules in category O and sheaves on moment graphs

Details Tilting modules in category O and sheaves on moment graphs Tilting modules in category O and sheaves on moment graphs

2012-02-01

arxiv.org/abs/1202.0326v2

Mathematics

Representation Theory

18 pages; minor typos and changes in chapter 5.1

Scientific paper

We describe tilting modules of the deformed category O over a semisimple Lie algebra as certain sheaves on a moment graph associated to the corresponding block of category O. We prove that they map to Braden-MacPherson sheaves constructed along the reversed Bruhat order under Fiebig's localization functor. By this means, we get character formulas for tilting modules and explain how Soergel's result about the Andersen filtration gives a Koszul dual proof of the semisimplicity of subquotients of the Jantzen filtration.

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