Twisting conjecture for quantum groups from Weyl matrix models

Let a Weyl matrix model be a matrix model constructed from Weyl matrices, and let $PE$ denote the associated quantum group appearing in the untwisted comparison model. Weyl-model twisting conjecture. The quantum group associated to a Weyl matrix model should appear as a suitable twist of $PE$. In the Fourier-cocycle situation, the main-character distribution agrees with that of $PE$; the conjecture proposes an underlying quantum-group relation, but the source does not specify the twist precisely.