Conjecture on uniqueness of conformal-block solutions of the Macdonald–Ruijsenaars equations

Let $\vec\Lambda\in\mathbb Z_{\ge0}^n[2{\mathfrak m}]$, and let $\mathbb M_\Theta$ be the Macdonald–Ruijsenaars operator acting on $L_{\vec\Lambda}[0]$-valued trigonometric polynomials. The space $\operatorname{Conf}_{\vec\Lambda}$ is spanned by the Weyl anti-symmetric hypergeometric conformal blocks $\vartheta^{\vec m}(\lambda)$. Generic conformal-block uniqueness conjecture. If $\vartheta(\lambda)$ is a Weyl anti-symmetric $L_{\vec\Lambda}[0]$-valued trigonometric polynomial satisfying

$$\mathbb M_\Theta\vartheta(\lambda)=(\dim_q L_\Theta)\vartheta(\lambda),$$

then $\vartheta(\lambda)\in\operatorname{Conf}_{\vec\Lambda}$. The conformal blocks are known to satisfy these equations, and the conjecture asserts that they exhaust the trigonometric polynomial solutions; its general validity remains open.