Combinatorial auslander-reiten quivers and reduced expressions

Se Jin Oh, Uhi Rinn Suh

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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
Volume56
Issue number2
DOIs
StatePublished - 2019

Keywords

  • And phrases
  • Combinatorial AR-quiver
  • Reduced expressions

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