The exterior-square CY(5) conjecture

Let ${\cal P}={\cal P}(\theta,z)$ be a CY(4)-operator, and let ${\cal Q}$ be the fifth-order differential operator constructed from ${\cal P}$ by requiring that, for any two linearly independent solutions $y_1,y_2$ of ${\cal P}y=0$, the function

$$w=z\left|\begin{array}{cc}y_1 & y_2 \\ y_1' & y_2'\end{array}\right|$$

is a solution of ${\cal Q}w=0$. The operator ${\cal Q}$ is said to satisfy the third condition of CY(5) when it has an integral power series solution. The exterior-square CY(5) conjecture. The differential operator ${\cal Q}$, constructed from a CY(4)-operator ${\cal P}$ as above, satisfies the third condition of CY(5). In all examples considered in the source, this condition holds, but a general proof is not known; if the conjecture holds, then ${\cal Q}$ is a CY(5)-operator.