Large-$N$ commutation-relation conjecture for the Chern–Simons matrix model

For $p\geq 2$, let $\tilde{J}^a_{b;n,m}$ and $\tilde{t}_{n,m}$ be the rescaled operators defined by

$$\tilde{J}^a_{b;m,n}=\left(\frac{k+p}{p}N\right)^{-\frac{m+n}{2}}J^a_{b;m,n},\qquad \tilde{t}_{m,n}=\left(\frac{k+p}{p}N\right)^{-\frac{m+n+2\delta_{m,n}}{2}}t_{m,n}.$$

Large-$N$ commutation-relation conjecture. In the large $N$ limit, these operators satisfy

$$[\tilde{J}^{a}_{b;n,m},\tilde{J}^{c}_{d;r,s}]\mathbin{\longrightarrow}\delta^{c}_{b}\tilde{J}^{a}_{d;n+r,m+s}-\delta^{a}_{d}\tilde{J}^{c}_{b;n+r,m+s}+k\delta_{n+r,m+s}\left(\delta^a_d\delta^c_b-\frac{1}{p}\delta^c_d\delta^a_b\right)(ns-mr)\frac{k+p}{p}\tilde{t}_{n+r-1,m+s-1},$$ $$[\tilde{t}_{n,m},\tilde{J}^{a}_{b;r,s}]\mathbin{\longrightarrow}0,$$ $$[\tilde{t}_{n,m},\tilde{t}_{r,s}]\mathbin{\longrightarrow}\delta_{n+r,m+s}(ns-mr)\tilde{t}_{n+r-1,m+s-1}.$$

The paper states that this conjecture follows from the preceding convergence conjecture. Its validity is therefore open.