Let $T(u)$ be the generating matrix of the Yangian $Y(\mathfrak{gl}_n)$ of $\mathfrak{gl}_n$. So we have the identity $[T_{ij}(u),T_{kl}(v)]=\frac{1}{u-v}(T_{kj}(u)T_{il}(v)-T_{kj}(v)T_{il}(u))$.
We can consider the matrix $T(z)e^{-\partial_z}$. It is written in https://arxiv.org/pdf/0711.2236.pdf#page12 that this matrix is Manin matrix (see https://en.m.wikipedia.org/wiki/Manin_matrix) but the proof is not given.
Question: how to prove this fact?