  In this paper, we introduce the notion of combinatorial Auslander-Reiten(AR)
quiver for commutation classes $[\widetilde{w}]$ of $w$ in finite Weyl group.
This combinatorial object visualizes the convex partial order
$\prec_{[\widetilde{w}]}$ on the subset $\Phi(w)$ of positive roots. By
analyzing properties of the combinatorial AR-quivers with labelings and
reflection maps, we can apply their properties to the representation theory of
KLR algebras and multiplication structure of dual PBW generators associated to
any commutation class $[\widetilde{w}_0]$ of the longest element $w_0$.
