a generalized Jucys–Murphy sequence (GJM-sequence) in the MFF {An | n ≥ 0} if Xn = J1, . . . , Jn , for all n ∈ N. If the ﬁeld k is inﬁnite then a GJM-sequence must exist. We can check whether or not a given sequence is a GJM-sequence by means of the content eigenvalues cT = (cT(1), . . . , cT(n)) of J1, . . . , Jn. (Note: cT(k) is the eigenvalue of Jk on the Gelfand–Tsetlin basis element vT.) To be precise, Proposition For a sequence (Jk ∈ Xk)k∈N in a MFF, the following are equivalent. 1 J1, . . . , Jn = Xn. 2 For all S, T ∈ Tab(n), S = T ⇐⇒ cS = cT. This is proved by a “Lagrange interpolation” argument. (Such arguments have appeared before, in work of [Murphy], [Diaconis–Greene], [Ram], etc.)