2016/05/16 by A. Mironov, A. Morozov, An. Morozov +1 · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math.GT #math.QA
paper · pdf · doi:10.1016/j.physletb.2016.06.041
published as Physics Letters B760 (2016) 45-58 · 16 pages
arxiv created 2016/05/16 · arxiv updated 2016/06/30
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\longrightarrow R with R⊗ (R ⊗ R) \longrightarrow R and (R⊗ R) ⊗ R \longrightarrow R with R⊗ ( R ⊗ R) \longrightarrow 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.