The differential resultant conjecture for commuting matrix ordinary differential operators

Let $K$ be a differential field whose field of constants $C$ is algebraically closed and has characteristic zero. Let $L$ and $B$ be commuting matrix ordinary differential operators with coefficients in $M_{\ell}(K)$, of respective orders $1$ and $n\geq 1$, as in the definition of these operators. Differential resultant conjecture. The differential resultant is a Burchnall–Chaundy polynomial; that is,

$$f(L,B)=0.$$

The conjecture is motivated by results for commuting matrix ordinary differential operators with analytic coefficients and by the verification of the claim for the first case of the AKNS hierarchy. Its proof is described as a challenging open problem.