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DISTRIBUTION OF ACCUMULATION POINTS OF ROOTS FOR TYPE (n - 1, 1) COXETER GROUPS

Part of: Algebraic combinatorics Special aspects of infinite or finite groups Metric geometry

Published online by Cambridge University Press:  01 March 2018

AKIHIRO HIGASHITANI ,
RYOSUKE MINEYAMA  and
NORIHIRO NAKASHIMA
AKIHIRO HIGASHITANI
Affiliation:
Department of Mathematics, Kyoto Sangyo University, Kamigamo Motoyama, Kita-ku, Kyoto 603-8555, Japan email ahigashi@cc.kyoto-su.ac.jp
RYOSUKE MINEYAMA
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan email r-mineyama@cr.math.sci.osaka-u.ac.jp
NORIHIRO NAKASHIMA
Affiliation:
Department of Mathematics, Tokyo Denki University, Tokyo 120-8551, Japan email nakashima@mail.dendai.ac.jp
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Abstract

In this paper, we investigate the set of accumulation points of normalized roots of infinite Coxeter groups for certain class of their action. Concretely, we prove the conjecture proposed in [6, Section 3.2] in the case where the equipped Coxeter matrices are of type $(n-1,1)$, where $n$ is the rank. Moreover, we obtain that the set of such accumulation points coincides with the closure of the orbit of one point of normalized limit roots. In addition, in order to prove our main results, we also investigate some properties on fixed points of the action.

MSC classification

Primary: 20F55: Reflection and Coxeter groups 51F15: Reflection groups, reflection geometries
Secondary: 05E15: Combinatorial aspects of groups and algebras
Type
Article
Information
Nagoya Mathematical Journal , Volume 235 , September 2019 , pp. 127 - 157
Copyright
© 2018 Foundation Nagoya Mathematical Journal  

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Footnotes

The first author is supported by JSPS Research Fellowship for Young Scientists.

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