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=3n=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.