Combinatorial auslander-reiten quivers and reduced expressions

Se Jin Oh, Uhi Rinn Suh

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In this paper, we introduce the notion of combinatorial Auslander-Reiten (AR) quivers for commutation classes [ ˜w] of w in a finite Weyl group. This combinatorial object is the Hasse diagram of the convex partial order ≺ [ ˜w] on the subset Φ(w) of positive roots. By analyzing properties of the combinatorial AR-quivers with labelings and reflection functors, we can apply their properties to the representation theory of KLR algebras and dual PBW-basis associated to any commutation class [˜w 0 ] of the longest element w 0 of any finite type.

Original languageEnglish
Pages (from-to)353-385
Number of pages33
JournalJournal of the Korean Mathematical Society
Issue number2
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019 Korean Mathematical Society.


  • And phrases
  • Combinatorial AR-quiver
  • Reduced expressions


Dive into the research topics of 'Combinatorial auslander-reiten quivers and reduced expressions'. Together they form a unique fingerprint.

Cite this