  The Murphy operators in the Hecke algebra H_n of type A are explicit
commuting elements, whose symmetric functions are central in H_n. In [Skein
theory and the Murphy operators, J. Knot Theory Ramif. 11 (2002), 475-492] I
defined geometrically a homomorphism from the Homfly skein C of the annulus to
the centre of each algebra H_n, and found an element P_m in C, independent of
n, whose image, up to an explicit linear combination with the identity of H_n,
is the m-th power sum of the Murphy operators. The aim of this paper is to give
simple geometric representatives for the elements P_m, and to discuss their
role in a similar construction for central elements of an extended family of
algebras H_{n,p}.
