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arXiv · 1509.04820

Combinatorial Auslander-Reiten quivers and reduced expressions

Se-Jin Oh·Uhi Rinn Suh
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Abstract

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 $w_0$.

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BibTeXRIS

Se-Jin Oh, Uhi Rinn Suh. 2015-09-16. Combinatorial Auslander-Reiten quivers and reduced expressions. https://arxiv.org/abs/1509.04820

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