Conjectural duality for intertwining operators of quasi-lisse vertex superalgebras

Let $V$ be a quasi-lisse vertex superalgebra. Let $W_1$ and $W_2$ be finitely strongly generated $V$-modules, let $W_0$ and $W_3$ be ordinary $g$-twisted modules, let $W_4$ and $W_6$ be weak $g$-twisted modules, and let $W_5$ be a weak $V$-module. Let $\mathcal{Y}_1, \mathcal{Y}_2, \mathcal{Y}_3, \mathcal{Y}_4, \mathcal{Y}_5, \mathcal{Y}_6$ be intertwining operators of types

$$\binom{W_0'}{W_1\;W_4},\binom{W_4}{W_2\;W_3},\binom{W_5}{W_1\;W_2},\binom{W_0'}{W_5\;W_3},\binom{W_0'}{W_2\;W_6},\binom{W_6}{W_1\;W_3},$$

respectively. For $w_1\in W_1$, $w_2\in W_2$, $w_3\in W_3$, and $w_0\in W_0'$, the relevant products and iterates are required to be interpreted as matrix coefficients of intertwining operators.

Duality conjecture. There exists a maximally extended multivalued analytic function $f(z_1,z_2;w_1,w_2,w_3,w_4)$ on

$$\{(z_1,z_2)\mid z_i\neq 0,\;z_i\neq z_j,\;i\neq j\}$$

such that the three series

$$\langle w_0,\mathcal{Y}(w_1,z_1)\mathcal{Y}(w_2,z_2)w_3\rangle,$$ $$\langle w_0,\mathcal{Y}_4(\mathcal{Y}_3(w_1,z_1-z_2)w_2,z_2)w_3\rangle,$$ $$(-1)^{|w_1||w_2|}\langle w_0,\mathcal{Y}_5(w_2,z_2)\mathcal{Y}_6(w_1,z_1)w_3\rangle$$

are absolutely convergent in the respective regions $|z_1|>|z_2|>0$, $|z_2|>|z_1-z_2|>0$, and $|z_2|>|z_1|>0$, and converge there to branches of $f(z_1,z_2;w_1,w_2,w_3,w_4)$.

This is a multivalued analytic formulation of duality for intertwining operators, extending associativity and commutativity-type analytic continuation to the quasi-lisse setting. The supplied text gives no resolution status, so the assertion is recorded as open.