Monodromy generation conjecture for the trigonometric Casimir connection

Let $\mathbf{B}_{\mathbf{m}}(z)$ denote the operator associated with the parameter $\mathbf{m}$ in the trigonometric Casimir connection, and define

$$\mathbf{B}_{\mathbf{m}}:=\lim_{z\rightarrow\infty}\mathbf{B}_{\mathbf{m}}(z).$$

Consider the monodromy representation of the trigonometric Casimir connection with base point around $0$.

Monodromy generation conjecture. The monodromy representation is generated by the operator $\mathbf{B}_{\mathbf{m}}$.

The statement is proposed as a description of the monodromy representation associated with the trigonometric Casimir connection. The supplied text gives no resolution evidence, so its status remains open.