Weighted L 2 -cohomology of Coxeter groups
By Michael W. Davis, J. Dymara, Tadeusz Januszkiewicz, B. Okun. 2004
59 citations recorded by the source corpus.
Given a Coxeter system .W;S/ and a positive real multiparameter q, we study the “weighted L 2 ‐cohomology groups,” of a certain simplicial complex † associated to .W;S/. These cohomology groups are Hilbert spaces, as well as modules over the Hecke algebra associated to .W;S/ and the multiparameter q. They have a “von Neumann dimension” with respect to the associated “Hecke‐von Neumann algebra” Nq. The dimension of the i‐th cohomology group is denoted b i .†/. It is a nonnegative real number which varies continuously with q. When q is integral, the b i .†/ are the usual L 2 ‐Betti numbers of buildings of type .W;S/ and thickness q. For a certain range of q, we calculate these cohomology groups as modules over Nq and obtain explicit formulas for the b i .†/. The range of q for which our calculations are valid depends on the region of convergence of the growth series of W . Within this range, we also prove a Decomposition Theorem for Nq, analogous to a theorem of LSolomon on the decomposition of the group algebra of a finite Coxeter group.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6f22491a5b7e4fc3a32060d93cc65bf13b1a7e4e
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Cohomology computations for Artin groups, Bestvina-Brady groups, and graph products (2010, methodology): “The calculations in (3c), (3d) and (4b) come from a different direction based on [13] and [15].”