Actions and irreducible representations of the mapping class group

Let G be a countable discrete group. Call two subgroups and of G commensurable if has finite index in both and . We say that an action of G on a discrete set X has noncommensurable stabilizers if the stabilizers of any two distinct points of X are not commensurable. We prove in this paper that the action of the map ping class group on the complex of curves has noncommensurable stabilizers. Following a method due to Burger and de la Harpe, this action leads to constructions of irreducible unitary representations of the mapping class group. Received: 26 July 1999 / Revised version: 14 May 2001 / Published online: 19 October 2001