The canonical symmetrizing form conjecture for complex reflection group Hecke algebras

Let $W$ be a finite complex reflection group, let $W'$ be a parabolic subgroup, and let ${\mathcal H}(W)$ be the associated Hecke algebra. A canonical symmetrizing form on ${\mathcal H}(W)$ is the form satisfying the properties whose uniqueness was established by Broué, Malle and Michel. Canonical symmetrizing form conjecture. The canonical symmetrizing form on ${\mathcal H}(W)$ exists, and its restriction to every parabolic subalgebra ${\mathcal H}(W')$ is the canonical symmetrizing form. The source notes that existence is not known in general, although constructions are available for complex reflection groups of rank $2$ and for groups of higher rank; the conjecture is known for Weyl groups only in the later centre-related result, not as a general resolution of this existence statement.