Differential expansion and rectangular HOMFLY for the figure eight knot
Differential expansion (DE) for a Wilson loop average in representation R is built to respect degenerations of representations for small groups. At the same time it behaves nicely under some changes of the loop, e.g. of some knots in the case of 3d Chern–Simons theory. Especially simple is the relat...
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| Format: | Article |
| Language: | English |
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Elsevier
2016-10-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321316302577 |
| _version_ | 1823933006683832320 |
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| author | A. Morozov |
| author_facet | A. Morozov |
| author_sort | A. Morozov |
| collection | DOAJ |
| description | Differential expansion (DE) for a Wilson loop average in representation R is built to respect degenerations of representations for small groups. At the same time it behaves nicely under some changes of the loop, e.g. of some knots in the case of 3d Chern–Simons theory. Especially simple is the relation between the DE for the trefoil 31 and for the figure eight knot 41. Since arbitrary colored HOMFLY for the trefoil are known from the Rosso–Jones formula, it is therefore enough to find their DE in order to make a conjecture for the figure eight. We fulfill this program for all rectangular representation R=[rs], i.e. make a plausible conjecture for the rectangularly colored HOMFLY of the figure eight knot, which generalizes the old result for totally symmetric and antisymmetric representations. |
| first_indexed | 2024-12-16T22:00:16Z |
| format | Article |
| id | doaj.art-11a6493adac34d7abfb04e8721d77ef3 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 1873-1562 |
| language | English |
| last_indexed | 2024-12-16T22:00:16Z |
| publishDate | 2016-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-11a6493adac34d7abfb04e8721d77ef32022-12-21T22:14:38ZengElsevierNuclear Physics B0550-32131873-15622016-10-01911C58260510.1016/j.nuclphysb.2016.08.027Differential expansion and rectangular HOMFLY for the figure eight knotA. Morozov0ITEP, Moscow 117218, RussiaDifferential expansion (DE) for a Wilson loop average in representation R is built to respect degenerations of representations for small groups. At the same time it behaves nicely under some changes of the loop, e.g. of some knots in the case of 3d Chern–Simons theory. Especially simple is the relation between the DE for the trefoil 31 and for the figure eight knot 41. Since arbitrary colored HOMFLY for the trefoil are known from the Rosso–Jones formula, it is therefore enough to find their DE in order to make a conjecture for the figure eight. We fulfill this program for all rectangular representation R=[rs], i.e. make a plausible conjecture for the rectangularly colored HOMFLY of the figure eight knot, which generalizes the old result for totally symmetric and antisymmetric representations.http://www.sciencedirect.com/science/article/pii/S0550321316302577 |
| spellingShingle | A. Morozov Differential expansion and rectangular HOMFLY for the figure eight knot Nuclear Physics B |
| title | Differential expansion and rectangular HOMFLY for the figure eight knot |
| title_full | Differential expansion and rectangular HOMFLY for the figure eight knot |
| title_fullStr | Differential expansion and rectangular HOMFLY for the figure eight knot |
| title_full_unstemmed | Differential expansion and rectangular HOMFLY for the figure eight knot |
| title_short | Differential expansion and rectangular HOMFLY for the figure eight knot |
| title_sort | differential expansion and rectangular homfly for the figure eight knot |
| url | http://www.sciencedirect.com/science/article/pii/S0550321316302577 |
| work_keys_str_mv | AT amorozov differentialexpansionandrectangularhomflyforthefigureeightknot |