QUANTUM INVARIANTS GIVEN BY EVALUATION OF KNOT POLYNOMIALS

MORTON, HR (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
Uncontrolled Keywords:	4902 Mathematical Physics, 4904 Pure Mathematics, 49 Mathematical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	23 Jan 2017 10:04
Last Modified:	22 Jun 2024 05:09
DOI:	10.1142/s021821659300012x
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3005314