Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213223649