Power sums and Homfly skein theory

The Murphy operators in the Hecke algebra Hn of type A are explicit commuting elements, whose symmetric functions are central in Hn. In [8] I defined geometrically a homomorphism from the Homfly skein C of the annulus to the centre of each algebra Hn, and found an element Pm in C, independent of n, whose image, up to an explicit linear combination with the identity of Hn, is the mth power sum of the Murphy operators. The aim of this paper is to give simple geometric representatives for the elements Pm, and to discuss their role in a similar construction for central elements of an extended family of algebras Hn,p.