2018/01/29 by C. Bai, Chuanzhi Bai, J. Jiang +10
Chemistry · Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Colored #Combinatorics #Computer science #Conjecture #Eigenvalues and eigenvectors #Geometric and Algebraic Topology #Knot (papermaking) #Knot theory #Mathematics #Molecular spectroscopy and chirality #Physics #Pure mathematics #Quantum #Quantum mechanics #Set (abstract data type) #hep-th #math.GT #math.QA
paper · pdf · doi:10.1016/j.geomphys.2018.05.020
published as Journal of Geometry and Physics, 132 (2018) 155-180 · 29 pages, 3 figures
arxiv created 2018/01/29 · openalex publication_date 2018/06/15 · arxiv updated 2018/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper is a next step in the project of systematic description of colored knot and link invariants started in previous papers. In this paper, we managed to explicitly find the inclusive Racah matrices, i.e. the whole set of mixing matrices in channels R1⊗ R2⊗ R3\longrightarrow Q with all possible Q, for |R|≤ 3. The calculation is made possible by use of the highest weight method. The result allows one to evaluate and investigate colored polynomials for arbitrary 3-strand knots and links and to check the corresponding eigenvalue conjecture. Explicit answers for Racah matrices and colored polynomials for 3-strand knots up to 10 crossings are available at http://knotebook.org. Using the obtained inclusive Racah matrices, we also calculated the exclusive Racah matrices with the help of trick earlier suggested in the case of knots. This method is proved to be effective and gives the exclusive Racah matrices earlier obtained by another method.