CELLS AND CACTI

Cédric Bonnafé (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

Let $(W,S)$ be a Coxeter system, let $\ph$ be a weight function on $S$ and let $\cactus_W$ denote the associated {\it cactus group}. Following an idea of I. Losev, we construct an action of $\cactus_W \times \cactus_W$ on $W$ which has nice properties with respect to the partition of $W$ into left, right or two-sided cells (under some hypothesis, which hold for instance if $\ph$ is constant or if $W$ is finite of rank $\le 4$). It must be noticed that the action depends heavily on $\ph$.

Domaines: Théorie des représentations [math.RT]

Cédric Bonnafé. CELLS AND CACTI. 2015. ⟨hal-01168198v1⟩