15 citations · 35 across the 7 of their papers we have counts for
7 papers
Affine reflection subgroups of Coxeter groups
Xiang Fu, Lawrence Reeves, Linxiao Xu
In this paper we study affine reflection subgroups in arbitrary infinite Coxeter groups of finite rank. In particular, we study the distribution of roots of Coxeter groups in the r…
Neighbourhoods in root systems of infinite Coxeter groups
Yuhan Cai, Xiang Fu, Lawrence Reeves
Let be a finitely generated infinite Coxeter group, with and being the corresponding root system and set of simple roots respectively. It has been observed by Hohlweg e…
Mapping the Davis complex into the imaginary cone
Xiang Fu, Lawrence Reeves
The study of the set of limit roots associated to an infinite Coxeter group was initiated by Hohlweg, Labbé and Ripoll and further developed by Dyer, Hohlweg, Péaux and Ripoll. The…
On paired root systems of Coxeter groups
Xiang Fu
This paper examines a systematic method to construct a pair of (inter-related) root systems for arbitrary Coxeter groups from a class of non-standard geometric representations. Thi…
Non-orthogonal geometric realizations of Coxeter groups
Xiang Fu
We define in an axiomatic fashion a \emph{Coxeter datum} for an arbitrary Coxeter group . This Coxeter datum will specify a pair of reflection representations of in two vect…
Coxeter groups, imaginary cones and dominance
Xiang Fu
Brink and Howlett have introduced a partial ordering, called dominance, on the positive roots in the Tits realization of Coxeter groups (Math. Ann. 296 (1993), 179--190). Recently…