  The oriented framed Homfly skein C of the annulus provides the natural
parameter space for the Homfly satellite invariants of a knot. It contains a
submodule C+ isomorphic to the algebra of the symmetric functions.
  We collect and expand formulae relating elements expressed in terms of
symmetric functions to Turaev's geometrical basis of C+. We reformulate the
formulae of Rosso and Jones for quantum sl(N) invariants of cables in terms of
plethysms of symmetric functions, and use the connection between quantum sl(N)
invariants and C+ to give a formula for the satellite of a cable as an element
of C+. We then analyse the case where a cable is decorated by the pattern which
corresponds to a power sum in the symmetric function interpretation of C+ to
get direct relations between the Homfly invariants of some diagrams decorated
by power sums.
