A new integral basis for the centre of the Iwahori–Hecke algebra of type A

We describe a recursive algorithm that produces an integral basis for the centre of the Iwahori–Hecke algebra of type A consisting of linear combinations of monomial symmetric polynomials of Jucys–Murphy elements. We also discuss the existence of integral bases for the centre of the Iwahori–Hecke algebra that consist solely of monomial symmetric polynomials of Jucys–Murphy elements. Finally, for n=3, we show that only one such basis exists for the centre of the Iwahori–Hecke algebra, by proving that there are exactly four bases for the centre of the corresponding symmetric group algebra which consist solely of monomial symmetric polynomials of Jucys–Murphy elements.