Locations of modules for Brauer tree algebras

Suppose Lambda is a Brauer tree algebra. We determine the location of a Lambda-module M in the stable Auslander-Reiten quiver of Lambda from the description of M as a multi-pushout of elementary modules. This is done by introducing a new combinatorial object associated to M, which is a certain walk around the Brauer tree of Lambda. These walks have applications to determining universal deformation rings and stable homomorphism groups. (C) 2002 Elsevier Science B.V. All rights reserved.