  Let Q be a quiver of type ADE. We construct the corresponding
Auslander-Reiten quiver as a topological complex inside the Coxeter complex
associated with the underlying Dynkin diagram. We use the notion of chamber
weights coming from the theory of the canonical basis of quantized envelopping
algebras, and show this set has a special linearity property in our setting.
Finally, we consider A_n case, and describe how Auslander-Reiten quivers
correspond to particular wiring diagrams.
