QUANTUM INVARIANTS GIVEN BY EVALUATION OF KNOT POLYNOMIALS



MORTON, HR ORCID: 0000-0002-8524-2695
(1993) QUANTUM INVARIANTS GIVEN BY EVALUATION OF KNOT POLYNOMIALS. Journal of Knot Theory and Its Ramifications, 02 (02). pp. 195-209.

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Abstract

<jats:p> It is shown that the knot invariant arising from an irreducible representation of a quantum group is, under certain conditions, an evaluation of the Homfly or Dubrovnik polynomial of the knot. </jats:p><jats:p> Besides the known cases of the fundamental representation for each of the quantum groups in the series A<jats:sub>n</jats:sub>, B<jats:sub>n</jats:sub>, C<jats:sub>n</jats:sub> and D<jats:sub>n</jats:sub>, the results cover the special cases of the 3-dimensional representation of SU(2) and the 6-dimensional representation of SU(4), which can be viewed as the fundamental representations of SO(3) and SO(6) respectively. The second of these cases leads to a new relation between an evaluation of the Dubrovnik polynomial of a knot and an evaluation of the Homfly polynomials of two 2-cables about the knot. </jats:p>

Item Type: Article
Depositing User: Symplectic Admin
Date Deposited: 23 Jan 2017 10:04
Last Modified: 19 Jan 2023 07:20
DOI: 10.1142/s021821659300012x
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3005314