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We describe a recursive algorithm that produces an integral basis for thecentre of the Hecke algebra of type A consisting of linear combinations ofmonomial symmetric polynomials of Jucys--Murphy elements. We also discuss theexistence of integral bases for the centre of the Hecke algebra that consistsolely 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 Heckealgebra, by proving that there are exactly four bases for the centre of thecorresponding symmetric group algebra which consist solely of monomialsymmetric polynomials of Jucys--Murphy elements.

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