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Journal of Operator Theory

Volume 89, Issue 2, Spring 2023  pp. 429-476.

Topological boundaries of connected graphs and Coxeter groups

Authors:  Mario Klisse
Author institution: EWI/DIAM, Technical University Delft, Delft, 2600 GA, The Netherlands

Summary:  We introduce and study certain topological spaces associated with connected rooted graphs. These spaces reflect combinatorial and order theoretic properties of the underlying graph and relate in the case of hyperbolic graphs to Gromov's hyperbolic compactification. They are particularly tractable in the case of Cayley graphs of finite rank Coxeter systems and are intimately related to the corresponding Iwahori-Hecke algebras. We study this connection by considering dynamical properties of the induced action of the Coxeter group.

Keywords:  Coxeter groups, Iwahori-Hecke algebras, topological boundaries, topological compactifications, graphs

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