{Twisted Poincaré Series and Geometric Factorization of Affine Weyl Groups

Abstract

We study the relation between the alternating product of twisted Poincar'e series of parabolic subgroups of affine Weyl groups and hyperbolic stabilizers of geodesic tubes. Moreover, from such relation, we find a length-preserving factorization of affine Weyl groups of type Ãn and Cn .