McGerty's center conjecture for cyclotomic Hecke algebras

Let $q$ be a parameter with $q\neq 1$, and let the cyclotomic Hecke algebra have its Jucys–Murphy center and center. McGerty's center conjecture. The Jucys–Murphy center of the cyclotomic Hecke algebra coincides with its center. The conjecture is known in some cases but remains open in general.