English

Cyclically reduced elements in Coxeter groups

Group Theory 2021-12-09 v4

Abstract

Let WW be a Coxeter group. We provide a precise description of the conjugacy classes in WW, in the spirit of Matsumoto's theorem. This extends to all Coxeter groups an important result on finite Coxeter groups by M. Geck and G. Pfeiffer from 1993. In particular, we describe the cyclically reduced elements of WW, thereby proving a conjecture of A. Cohen from 1994.

Keywords

Cite

@article{arxiv.1812.02543,
  title  = {Cyclically reduced elements in Coxeter groups},
  author = {Timothée Marquis},
  journal= {arXiv preprint arXiv:1812.02543},
  year   = {2021}
}

Comments

16 pages, 2 figures; to appear in Annales scientifiques de l'Ecole normale sup\'erieure