Racah matrices and hidden integrability in evolution of knots
We construct a general procedure to extract the exclusive Racah matrices S and S¯ from the inclusive 3-strand mixing matrices by the evolution method and apply it to the first simple representations R=[1], [2], [3] and [2,2]. The matrices S and S¯ relate respectively the maps (R⊗R)⊗R¯⟶R with R⊗(R⊗R¯...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2016-09-01
|
| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269316302945 |
| Summary: | We construct a general procedure to extract the exclusive Racah matrices S and S¯ from the inclusive 3-strand mixing matrices by the evolution method and apply it to the first simple representations R=[1], [2], [3] and [2,2]. The matrices S and S¯ relate respectively the maps (R⊗R)⊗R¯⟶R with R⊗(R⊗R¯)⟶R and (R⊗R¯)⊗R⟶R with R⊗(R¯⊗R)⟶R. They are building blocks for the colored HOMFLY polynomials of arbitrary arborescent (double fat) knots. Remarkably, the calculation realizes an unexpected integrability property underlying the evolution matrices. |
|---|---|
| ISSN: | 0370-2693 1873-2445 |