An unexpected property of $\mathbf{g}$-vectors for rank 3 mutation-cyclic quivers

Jihyun Lee, Kyungyong Lee

Let $Q$ be a rank 3 mutation-cyclic quiver. It is known that every $\mathbf{c}$-vector of $Q$ is a solution to a quadratic equation of the form $$\sum_{i=1}^3 x_i^2 + \sum_{1\leq i…