The fermionic-form identity between M and N

Let $W$ be the tensor product of finite-dimensional modules used to define the fermionic forms $M(W,\lambda,q)$, $M_l(W,q)$, and $N_l(W,\lambda,q)$, and let $N_\infty$ denote the limit form. For $\lambda\in\overline{P}^+$, consider the two forms $M(W,\lambda,q)$ and $N_\infty(W,\lambda,q)$.

M=N conjecture. The computer experiments suggest

$$M(W,\lambda,q)=N_\infty(W,\lambda,q)\quad\text{for }\lambda\in\overline{P}^+,$$

and

$$M_l(W,q)=N_l(W,0,q).$$

These identities relate fermionic forms based on different $q$-binomial conventions; the source presents them as experimental conjectures and gives no proof or resolution.