Boundary Casimir connection monodromy conjecture

Let $\mathfrak{h}^{\mathrm{reg}}$ be the regular locus for the Cartan subalgebra and let the boundary Casimir connection descend to the quotient $\mathfrak{h}^{\mathrm{reg}}/W$, where $W$ is the Weyl group. Its monodromy acts on the relevant integrable modules, and the quantum boundary Weyl group action is the action obtained from the quantum boundary Weyl group operators. Boundary Casimir monodromy conjecture. The monodromy of the boundary Casimir connection is given by the quantum boundary Weyl group action. This is proposed as the boundary analogue of the known description of the usual Casimir-connection monodromy by the quantum Weyl group action; the source does not state a proof or resolution.