Chern-Simons perturbative series revisited
A group-theoretical structure in a perturbative expansion of the Wilson loops in the 3d Chern-Simons theory with SU(N) gauge group is studied in symmetric approach. A special basis in the center of the universal enveloping algebra ZU(slN) is introduced. This basis allows one to present group factors...
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| Main Authors: | , , |
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| Format: | article |
| Language: | EN |
| Published: |
Elsevier
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/9947d24d95cf40c7b084d983905cb831 |
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| Summary: | A group-theoretical structure in a perturbative expansion of the Wilson loops in the 3d Chern-Simons theory with SU(N) gauge group is studied in symmetric approach. A special basis in the center of the universal enveloping algebra ZU(slN) is introduced. This basis allows one to present group factors in an arbitrary irreducible finite-dimensional representation. Developed methods have wide applications, the most straightforward and evident ones are mentioned. Namely, Vassiliev invariants of higher orders are computed, a conjecture about existence of new symmetries of the colored HOMFLY polynomials is stated, and the recently discovered tug-the-hook symmetry of the colored HOMFLY polynomial is proved. |
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