2016/11/11 by Sh. Shakirov, Shakirov, Sh., А. Слепцов +2 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT) #hep-th #math.GT #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.1611.03797
16 pages, 2 figures
openalex publication_date 2016/11/11 · arxiv created 2021/05/05 · arxiv updated 2021/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper is a next step in the project of systematic description of colored knot polynomials started in arXiv:1506.00339. In this paper, we managed to explicitly find the inclusive Racah matrices, i.e. the whole set of mixing matrices in channels R⊗ 3\longrightarrow Q with all possible Q, for R=[3,3]. The case R=[3,3] is a multiplicity free case as well as R=[2,2] obtained in arXiv:1605.03098. The calculation is made possible by the use of highest weight method with the help of Gelfand-Tseitlin tables. The result allows one to evaluate and investigate [3,3]-colored polynomials for arbitrary 3-strand knots, and this confirms many previous conjectures on various factorizations, universality, and differential expansions. With the help of a method developed in arXiv:1605.04881 we manage to calculate \it exclusive Racah matrices S and S in R=[3,3]. Our results confirm a calculation of these matrices in arXiv:1606.06015, which was based on the conjecture of explicit form of differential expansion for twist knots. Explicit answers for Racah matrices and [3,3]-colored polynomials for 3-strand knots up to 10 crossings are available at http://knotebook.org.