Murphy operators in Knot Theory

The Murphy operators in the Hecke algebra Hn are commuting elements which arose originally in an algebraic setting in connection with representation theory. They can be represented diagrammatically in a Homfly skein theory version of H-n. Symmetric functions of the Murphy operators are known to lie in the centre of Hn(.) Diagrammatic views of these are given which demonstrate their algebraic properties readily, and how analogous central elements can be constructed diagrammatically in some related algebras.