THE HOMFLY POLYNOMIAL OF THE DECORATED HOPF LINK

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 Homfly skein of the annulus by elements Qλ, depending on partitions λ. We show how the 2-variable Homfly invariant of the Hopf link arising from decorations Qλ and Qμ can be found from the Schur symmetric function sμ 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 Vλ and Vμ, which is a 1-variable specialisation of , can be expressed in terms of an N × N minor of the Vandermonde matrix (qij).