2012/11/24 by de Cornulier, Yves
#20B15 #46L05 #FOS: Mathematics #Group Theory (math.GR) #Primary 20F55 #Secondary 22E40
paper · doi:10.48550/arxiv.1211.5635
Let W be an irreducible, finitely generated Coxeter group. The geometric representation provides an discrete embedding in the orthogonal group of the so-called Tits form. One can look at the representation modulo the kernel of this form; we give a new proof of the following result of Vinberg: if W is non-affine, then this representation remains faithful. Our proof uses relative Kazhdan Property (T). The following corollary was only known to hold when the Tits form is non-degenerate: the reduced C*-algebra of W is simple with a unique normalized trace. Some other corollaries are pointed out.