A ug 2 00 1 The Homfly polynomial of the decorated Hopf link HUGH R . MORTON and SASCHA

The main goal is to find the Homfly polynomial of a link formed by decorating each component of the Hopf link with the closure of a directly oriented tangle. Such decorations are spanned in the Hom-fly skein of the annulus by elements Q λ , depending on partitions λ. We show how the 2-variable Homfly invariant λ, µ of the Hopf link arising from decorations Q λ and Q µ can be found from the Schur symmetric function s µ of an explicit power series depending on λ. We show also that the quantum invariant of the Hopf link coloured by irreducible sl(N) q modules V λ and V µ , which is a 1-variable speciali-sation of λ, µ, can be expressed in terms of an N × N minor of the Vandermonde matrix (q ij).