The combinatorics of Coxeter categories
Representation Theory
2010-06-07 v3 Combinatorics
Abstract
We present an alternative construction of Soergel's category of bimodules associated to a reflection faithful representation of a Coxeter system. We show that its objects can be viewed as sheaves on the associated moment graph. We introduce an exact structure and show that Soergel's "special" bimodules are the projective objects. Then we construct the indecomposable projectives by both a global and a local method, discuss a version of the Kazhdan-Lusztig conjecture and prove it for universal Coxeter systems.
Cite
@article{arxiv.math/0512176,
title = {The combinatorics of Coxeter categories},
author = {Peter Fiebig},
journal= {arXiv preprint arXiv:math/0512176},
year = {2010}
}
Comments
24 pages; minor revision, typos corrected. Final version to appear in Trans. Amer. Math. Soc