Maximal green sequences for exceptional mutation finite quivers.


The paper by Felikson, Shapiro, and Tumarkin gives a complete classification of quivers of finite mutation type that don't arise from triangulations of marked surfaces. Existence of a maximal green sequences for the quivers in the mutation class of Dynkin E6, E7, and E8 was shown in Theorem 4.1 in the paper by Brüstle Dupont and Pérotin. The quivers in the mutation class of X7 were shown not to have a maximal green sequence by Seven.

Here we give a list of maximal green sequences for every quiver in the exceptional finite mutation classes. We use the convention given above in Brüstle Dupont and Pérotin for our maximal green sequences. The format of the files below is the index of the quiver in the mutation class as generated by the b_matrix_class() function in the ClusterSeed package of Sage by the initial quiver in the list. Then we give the corresponding skew-symmetric matrix of the quiver followed by a sequence of vertices that give a maximal green sequence for the quiver. We break the large mutation classes into several files for convenience.

Affine E6

Quivers 0 - 131

Affine E7

Quivers 0 - 1079

Affine E8

Quivers 0 - 999   Quivers 1000 - 1999   Quivers 2000 - 2999   Quivers 3000 - 3999   Quivers 4000 - 4999   Quivers 5000 - 5999   Quivers 6000 - 6999   Quivers 7000 - 7559  

Extended Affine E6

Quivers 0 - 48

Extended Affine E7

Quivers 0 - 505

Extended Affine E8

Quivers 0 - 999   Quivers 1000 - 1999   Quivers 2000 - 2999   Quivers 3000 - 3999   Quivers 4000 - 4999   Quivers 5000 - 5738  

X6

Quivers 0 - 4