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Extremal elements in Coxeter groups and metric commensurators of Kac-Moody groups

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Abstract

We prove a characterization of irreducible, non-spherical and non-affine Coxeter groups, motivated by applications to metric commensurators of Kac-Moody groups and twinnings at finite distance.

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Acknowledgements

We thank Pierre-Emmanuel Caprace for pointing out to us that our results on twinnings can be applied to metric commensurators of Kac-Moody groups. We also thank the referee for his careful reading and valuable suggestions. The research for this paper was supported by the DFG through the Grant MU 1281/4-1. The second author is supported by the Fund for Scientific Research—Flanders (FWO—Vlaanderen).

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Authors and Affiliations

  1. Mathematisches Institut, Arndtstraße 2, 35392, Gießen, Germany

    Bernhard Mühlherr

  2. Department of Mathematics, Ghent University, Krijgslaan 281, S22, 9000, Ghent, Belgium

    Koen Struyve

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  1. Bernhard Mühlherr
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  2. Koen Struyve
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Correspondence to Koen Struyve.

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Mühlherr, B., Struyve, K. Extremal elements in Coxeter groups and metric commensurators of Kac-Moody groups. Math. Z. 288, 287–298 (2018). https://doi.org/10.1007/s00209-017-1888-x

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  • DOI: https://doi.org/10.1007/s00209-017-1888-x

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