Cyclically Reduced Elements in Coxeter Groups

par Prof. Timothée Marquis (Université Catholique de Louvain)

lundi 3 févr. 2020, 16:30 → 17:45 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Let W be a Coxeter group. We provide a precise description of the conjugacy classes in W, yielding an analogue of Matsumoto's theorem for the conjugacy problem in arbitrary Coxeter groups. 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 W, thereby proving a conjecture of A. Cohen from 1994.