[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j180190

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)

Publication Information

Journal of the Korean Mathematical Society / v.56, no.2, 2019 , pp. 353-385 More about this Journal

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.

Keywords

combinatorial AR-quiver; reduced expressions;

Citations & Related Records

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