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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
MathSciNet review:
2395170
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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.
References:
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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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