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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{fu2026dual,
  title = {{The dual of the Tits cone and dominance of Coxeter groups}},
  author = {Xiang Fu and Jiaqing Gu and Mengfan Lyu and Lawrence Reeves and Linxiao Xu and Shuyang Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14093},
  eprint = {2609.14093},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14093},
}
RIS
TY  - UNPB
TI  - The dual of the Tits cone and dominance of Coxeter groups
AU  - Xiang Fu
AU  - Jiaqing Gu
AU  - Mengfan Lyu
AU  - Lawrence Reeves
AU  - Linxiao Xu
AU  - Shuyang Zhao
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.14093
UR  - https://arxiv.org/abs/2609.14093
AB  - 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.
ER  -