The combinatorics of Coxeter categories
By P. Fiebig. 2005
71 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/b494e234377c4d1ebc744c95a77b1e987e76486e
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Singular Soergel bimodules (2010, background): “ned by Soergel in [32] (using a slightly different definition of B) and formed the principal motivation for this work. Similar ideas have also been pursued by Dyer in [6] and [7], and by Fiebig in [9], [10] and [11]. Of course, the most famous basis for the Hecke algebra with properties similar to the”
- The Hodge theory of Soergel bimodules (2012, unknown): “Soergel’s conjecture was established for dihedral groups by Soergel [Soe92] and for “universal” Coxeter systems (where each product of simple reflections has infinite order) by Fiebig [Fie08] and Libedinsky.”