Partial symmetry conjecture for elliptic corner VOA correlation functions

Let $\vec{c}=(c_1,\dots,c_n)=(1^L2^M3^N)$ and suppose that $q_{\vec{c}}\neq1$. Let $f^{\vec{c}}_{11}$ be the corresponding elliptic corner-VOA structure function and $\widetilde{T}^{\vec{c}}_1$ its current. A formal power series is partially symmetric with respect to sets of variables if it is invariant under permutations preserving each set. Partial symmetry conjecture. The function

$$\prod_{1\leq i<j\leq m}f^{\vec{c}}_{11}\left(\frac{z_j}{z_i};p\right)\langle0|\widetilde{T}^{\vec{c}}_1(z_1;p)\cdots\widetilde{T}^{\vec{c}}_1(z_m;p)|0\rangle$$

is symmetric in $z_1,\dots,z_m$ and partially symmetric with respect to the sets $\{u_1,\dots,u_L\}$, $\{u_{L+1},\dots,u_{L+M}\}$, and $\{u_{L+M+1},\dots,u_{L+M+N}\}$. This predicts the partially symmetric polynomial structure of general elliptic corner-VOA correlation functions; no resolution is supplied in the text.