Auslander-Reiten quivers and the Coxeter complex
Abstract
Description
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.
19 pages. Revised version of SDAD preprint 2001-25. Submitted to Algebra and Representation Theory. LaTeX2e, uses epic, eepic packages
19 pages. Revised version of SDAD preprint 2001-25. Submitted to Algebra and Representation Theory. LaTeX2e, uses epic, eepic packages