The combinatorics of Coxeter categories
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Open Access
- 14 March 2008
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 360 (08) , 4211-4233
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.Keywords
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