Dipper–James conjecture on the centre of the symmetric-group Hecke algebra

Let $R$ be a commutative ring with $1$, let $q\in R$ be invertible, and let ${\mathcal H}={\mathcal H}_n(R,q)$ be the Hecke algebra of the symmetric group, with Jucys–Murphy operators

$$L_i:=\sum_{1\le j<i}q^{j-i}T_{(j,i)}\quad (1\le i\le n).$$

Dipper–James conjecture. The centre of ${\mathcal H}$ is the set of symmetric polynomials in the Jucys–Murphy operators $L_1,\ldots,L_n$.

This identifies the centre with the algebra generated by symmetric functions of the Jucys–Murphy operators. The source presents it as a conjecture of Dipper and James; its resolution is not established by the supplied context.