Commutation of $U_0$ with the positive Heisenberg subalgebra

Let $H_{+}$ be the subalgebra generated by $1,B_1,B_2,\dots$, and let $U_0$ denote the operator acting on the level-1 module under consideration. At the specialization $p=q^{2n}$, the commutation conjecture.

$$[U_0,H_{+}]=0.$$

This conjecture is motivated by the Yangian limit and would imply that the specialized operator $U_0$ commutes with the positive Heisenberg subalgebra. The source does not establish whether the assertion holds.