Journal
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 360, Issue 8, Pages 4211-4233Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9947-08-04376-6
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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.
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