The dual of the Tits cone and dominance of Coxeter groups

Xiang Fu; Jiaqing Gu; Mengfan Lyu; Lawrence Reeves; Linxiao Xu; Shuyang Zhao

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arXiv · 2609.14093

The dual of the Tits cone and dominance of Coxeter groups

Xiang Fu·Jiaqing Gu·Mengfan Lyu·Lawrence Reeves·Linxiao Xu·Shuyang Zhao

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Abstract

In this paper we introduce a potentially infinite process of reflections applied to a sequence of points in the dual of the Tits cone associated with an arbitrary finitely generated infinite Coxeter group. This process is infinite whenever the starting point is not in the imaginary cone of the given Coxeter group. We show that this process exhibits well-defined asymptotic behaviour. We study the resulting limits, and give a characterisation of these limits. We then apply the techniques developed from this asymptotic process to the study of infinite sequences of roots totally ordered by the dominance partial ordering.

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BibTeX RIS

Xiang Fu, Jiaqing Gu, Mengfan Lyu, Lawrence Reeves, Linxiao Xu, Shuyang Zhao. 2026-09-12. The dual of the Tits cone and dominance of Coxeter groups. https://arxiv.org/abs/2609.14093

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