Auslander-Reiten quivers and the Coxeter complex

2002/08/13 by Shmuel Zelikson, Zelikson, Shmuel
Mathematics · #16G70 #17B10 #20F55 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16G70 #msc:17B10 #msc:20F55

paper · pdf · doi:10.48550/arxiv.math/0208098

19 pages. Revised version of SDAD preprint 2001-25. Submitted to Algebra and Representation Theory. LaTeX2e, uses epic, eepic packages

arxiv created 2002/08/13 · openalex publication_date 2002/08/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

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.

Related

• Coxeter Elements and Periodic Auslander-Reiten Quiver
• A categorification of combinatorial Auslander-Reiten quivers
• Twisted Coxeter elements and folded AR-quivers via Dynkin diagram\n automorphisms: I
• The Representation Theory of Dynkin Quivers. Three Contributions
• Abstract representation theory via coherent Auslander-Reiten diagrams