Geodesic
$C$-Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $Q$ be an acyclic quiver and $k$ be an algebraically closed field. The indecomposable exceptional modules of the path algebra $kQ$ have been widely studied. The real Schur roots of the root system associated to $Q$ are the dimension vectors of the indecomposable exceptional modules. It has been shown in [Nájera Chávez A., Int. Math. Res. Not. 2015 (2015), 1590–1600] that for acyclic quivers, the set of positive $c$-vectors and the set of real Schur roots coincide. To give a diagrammatic description of $c$-vectors, K-H. Lee and K. Lee conjectured that for acyclic quivers, the set of c-vectors and the set of roots corresponding to non-self-crossing admissible curves are equivalent as sets [Exp. Math., to appear, arXiv:1703.09113.]. In [Adv. Math. 340 (2018), 855–882], A. Felikson and P. Tumarkin proved this conjecture for 2-complete quivers. In this paper, we prove a revised version of Lee-Lee conjecture for acyclic quivers of type $A$, $D$, and $E_{6}$ and $E_7$.
Keywords: real Schur roots, $c$-vectors, non-self-crossing curves.
Mots-clés : acyclic quivers 
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     author = {Su Ji Hong},
     title = {$C${-Vectors} and {Non-Self-Crossing} {Curves} for {Acyclic} {Quivers} of {Finite} {Type}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a9/}
}
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Su Ji Hong. $C$-Vectors and Non-Self-Crossing Curves for Acyclic Quivers of Finite Type. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a9/

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