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Register a new userThe Homfly polynomial of the decorated Hopf link
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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 Q_lambda, depending on partitions lambda. We show how to find the 2-variable Homfly invariant <lambda,mu> of the Hopf link arising from decorations Q_lambda and Q_mu in terms of the Schur symmetric function s_mu of an explicit power series depending on lambda. We show also that the quantum invariant of the Hopf link coloured by irreducible sl(N)_q modules V_lambda and V_mu, which is a 1-variable specialisation of <lambda,mu>, can be expressed in terms of an N x N minor of the Vandermonde matrix (q^{ij}).
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