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Spectral representations of vertex transitive graphs, Archimedean solids and finite Coxeter groups

Ivrissimtzis, Ioannis; Peyerimhoff, Norbert

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Authors

Norbert Peyerimhoff



Abstract

In this article, we study eigenvalue functions of varying transitionprobability matrices on finite, vertex transitive graphs. We provethat the eigenvalue function of an eigenvalue of fixed highermultiplicity has a critical point if and only if the correspondingspectral representation is equilateral. We also show how thegeometric realisation of a finite Coxeter group as a reflectiongroup can be used to obtain an explicit orthogonal system ofeigenfunctions. Combining both results, we describe the behaviour ofthe spectral representations of the second highest eigenvaluefunction under the change of the transition probabilities in thecase of Archimedean solids.

Citation

Ivrissimtzis, I., & Peyerimhoff, N. (2013). Spectral representations of vertex transitive graphs, Archimedean solids and finite Coxeter groups. Groups, Geometry, and Dynamics, 7(3), 591-615. https://doi.org/10.4171/ggd/199

Journal Article Type Article
Acceptance Date Mar 19, 2012
Online Publication Date Aug 27, 2013
Publication Date Aug 27, 2013
Deposit Date Jun 17, 2019
Publicly Available Date Jun 17, 2019
Journal Groups, Geometry, and Dynamics
Print ISSN 1661-7207
Publisher EMS Press
Peer Reviewed Peer Reviewed
Volume 7
Issue 3
Pages 591-615
DOI https://doi.org/10.4171/ggd/199

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