Manchester Geometry Seminar 2001/2002

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. I will review this briefly and present a single tangle which represents their sum, and which is obviously central.

Symmetric functions of the Murphy operators are also central in H_n. I define geometrically a homomorphism from the skein of the annulus to the centre of each algebra H_n, and find an element in the skein, independent of n, whose image is the m^th power sum of the Murphy operators.