Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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COMBINATORIAL AUSLANDER-REITEN QUIVERS AND REDUCED EXPRESSIONS

  • Oh, Se-jin (Department of Mathematics Ewha Womans University) ;
  • Suh, Uhi Rinn (Department of Mathematical Sciences Research Institute of Mathematics Seoul National University)
  • Received : 2018.03.19
  • Accepted : 2018.07.31
  • Published : 2019.03.01
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Abstract

In this paper, we introduce the notion of combinatorial Auslander-Reiten (AR) quivers for commutation classes [${\tilde{w}}]$ of w in a finite Weyl group. This combinatorial object is the Hasse diagram of the convex partial order ${\prec}_{[{\tilde{w}}]}$ on the subset ${\Phi}(w)$ 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 [${\tilde{w}}_0$] of the longest element $w_0$ of any finite type.

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References

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