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The Homfly polynomial of the decorated Hopf link | | Hugh R. Morton
; Sascha G. Lukac
; | | Date: |
2 Aug 2001 | | Journal: | J. Knot Theory Ramif. 12 (2003), 395-416 | | Subject: | Geometric Topology MSC-class: 57M25 | math.GT | | Abstract: | 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 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 , can be expressed in terms of an N x N minor of the Vandermonde matrix (q^{ij}). | | Source: | arXiv, math.GT/0108011 | | Services: | Forum | Review | PDF | Favorites | |
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