Affine reflection subgroups of Coxeter groups

Autor:	Fu, Xiang, Reeves, Lawrence, Xu, Linxiao
Rok vydání:	2019
Předmět:	Mathematics - Group Theory Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	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 root subsystems associated with affine reflection subgroups. We give a characterization of limit roots arising from affine reflection subgroups. We also give a characterization of when a Coxeter group may possess affine reflection subgroups. We show that the intersection of the normalized isotropic cone (associated with the Tits representation of a Coxeter group) and the imaginary cone consists of limit roots closely related to affine reflection subgroups. Comment: The current version contains corrections to earlier versions, and it contains improved results. In the current version we show that each point in the intersection of the imaginary cone and the normalized isotropic cone is in fact a limit root relating to affine reflection subgroups
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1911.07237 Zobrazit plný text záznamu View this record from Arxiv