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The combinatorics of Coxeter categories

Author(s): Peter Fiebig
Journal: Trans. Amer. Math. Soc. 360 (2008), 4211-4233.
MSC (2000): Primary 20F55; Secondary 17B67
Posted: March 14, 2008
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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.

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Additional Information:

Peter Fiebig
Affiliation: Mathematisches Institut, Universit{ä}t Freiburg, 79104 Freiburg, Germany

DOI: 10.1090/S0002-9947-08-04376-6
PII: S 0002-9947(08)04376-6
Received by editor(s): July 18, 2006
Posted: March 14, 2008
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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