Skein theory and the Murphy operators

The Murphy operators in the Hecke algebra H-n of type A are explicit commuting elements whose sum generates the centre. They can be represented by simple tangles in the Homfly skein theory version of H-n. In this paper I present a single tangle which represents their sum, and which is obviously central. As a consequence it is possible to identify a natural basis for the Homfly skein of the annulus, C. Symmetric functions of the Murphy operators are also central in H-n. I define geometrically a homomorphism from C to the centre of each algebra H-n, and find an element in C, independent of n, whose image is the mth power sum of the Murphy operators. Generating function techniques are used to describe images of other elements of C in terms of the Murphy operators, and to demonstrate relations among other natural skein elements.