The graded-symmetry conjecture for the affine cyclotomic wreath product algebra

Let $A$ be the algebra appearing in the construction, let $n$ be a positive integer, and let $\mathcal{H}^{\mathbf{C}}_n(A)$ be its cyclotomic quotient.

Graded-symmetry conjecture. The algebra $\mathcal{H}^{\mathbf{C}}_n(A)$ is graded symmetric.

Graded symmetry would provide a strong structural property of this cyclotomic algebra. The supplied text gives no evidence that the conjecture has been resolved.