2015/06/25 by Cédric Bonnafé, Bonnafé, Cédric · 2 citations
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1506.07737
23 pages. This new version extends the scope of validity of the main result by removing an hypothesis. For this purpose, we have slightly extended some results of arXiv:1502.01661
arxiv created 2015/10/16 · arxiv updated 2015/10/19
Let (W,S) be a Coxeter system, let φ be a weight function on S and let Cact_W denote the associated \it cactus group. Following an idea of I. Losev, we construct an action of Cact_W × Cact_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 φ is constant or if W is finite of rank \textless 5). It must be noticed that the action depends heavily on φ.