The Homfly polynomial of the decorated Hopf link

Morton, HR ORCID: 0000-0002-8524-2695 and Lukac, SG (2003) The Homfly polynomial of the decorated Hopf link. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 12 (3). pp. 395-416.

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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 <\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}).

Item Type:	Article
Additional Information:	25 pages
Uncontrolled Keywords:	skein theory, Hopf link, Homfly polynomial, quantum sl(N) invariants, symmetric functions, Schur functions, annulus, Hecke algebras
Depositing User:	Symplectic Admin
Date Deposited:	23 Jan 2017 10:03
Last Modified:	07 Feb 2023 05:02
DOI:	10.1142/S0218216503002536
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3005316