MORTON, HR
(1993)
QUANTUM INVARIANTS GIVEN BY EVALUATION OF KNOT POLYNOMIALS.
Journal of Knot Theory and Its Ramifications, 02 (02).
pp. 195-209.
Text
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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 |
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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: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3005314 |