The center-surjectivity conjecture for cyclotomic quiver Hecke algebras

Let $A$ be a symmetric generalized Cartan matrix, and let $cGamma$ be its associated quiver with no loops. Let $cmathscr{R}_{cbeta}(cGamma)$ and $cmathscr{R}_{cbeta}^{cLambda}(cGamma)$ denote, respectively, the quiver Hecke algebra and cyclotomic quiver Hecke algebra associated with $cGamma$, for $cLambdacin P^+$ and $cbetacin Q_n^+$. Center-surjectivity conjecture. The center of $cmathscr{R}_{cbeta}(cGamma)$ maps surjectively onto the center of $cmathscr{R}_{cbeta}^{cLambda}(cGamma)$. This folklore conjecture would identify every central element of the cyclotomic quotient as the image of a central element in the corresponding quiver Hecke algebra; the supplied text gives no resolution, so its status remains open.