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. ISSN 0218-2165, 1793-6527

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Abstract

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. Besides the known cases of the fundamental representation for each of the quantum groups in the series An, Bn, Cn and Dn, 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.

Item Type:	Article
Uncontrolled Keywords:	4902 Mathematical Physics, 4904 Pure Mathematics, 49 Mathematical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	23 Jan 2017 10:04
Last Modified:	06 Dec 2024 22:37
DOI:	10.1142/s021821659300012x
Related Websites:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3005314
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