2016/12/31 by A. Morozov · 12 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic structures and combinatorial models #Antiparallel (mathematics) #Braid #Differential (mechanical device) #Factorization #Holomorphic and Operator Theory #Matrix (chemical analysis) #Matrix decomposition #Unitarity #hep-th #math-ph #math.GT #math.MP #math.QA
paper · pdf · doi:10.1142/s0217732318500621
published in Modern Physics Letters A 33(12), 1850062 (World Scientific) · 14 pages
openalex created_date 2016/12/16 · arxiv created 2016/12/31 · openalex publication_date 2018/04/17 · arxiv updated 2018/04/26 · openalex updated_date 2026/08/05
Factorization of the differential expansion (DE) coefficients for colored HOMFLY-PT polynomials of antiparallel double braids, originally discovered for rectangular representations [Formula: see text], in the case of rectangular representations [Formula: see text], is extended to the first non-rectangular representations [Formula: see text] and [Formula: see text]. This increases chances that such factorization will take place for generic [Formula: see text], thus fixing the shape of the DE. We illustrate the power of the method by conjecturing the DE-induced expression for double-braid polynomials for all [Formula: see text]. In variance with the rectangular case, the knowledge for double braids is not fully sufficient to deduce the exclusive Racah matrix [Formula: see text] — the entries in the sectors with nontrivial multiplicities sum up and remain unseparated. Still, a considerable piece of the matrix is extracted directly and its other elements can be found by solving the unitarity constraints.