Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed
arXiv:2205.12238 · doi:10.1140/epjc/s10052-022-10851-7
Abstract
For a peculiar family of double braid knots there is a remarkable factorization formula for the coefficients of the differential (cyclotomic) expansion (DE), which nowadays is widely used to construct the exclusive Racah matrices and in arbitrary representations. The origins of the factorization remain obscure and the special role of double braids remains a mystery. In an attempt to broaden the perspective, we extend the family of double braids to antiparallel triple pretzels, which are obtained by the defect-preserving deformation from the trefoil and all have defect zero. It turns out that factorization of DE coefficients is violated quite strongly, still remains described by an elegant formula, at least for all symmetric representations.
References in corpus (16)
- HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
- Character expansion for HOMFLY polynomials. III. All 3-Strand braids in the first symmetric representation
- Eigenvalue hypothesis for Racah matrices and HOMFLY polynomials for 3-strand knots in any symmetric and antisymmetric representations
- Superintegrability summary
- A unified Witten-Reshetikhin-Turaev invariant for integral homology spheres
- On colored HOMFLY polynomials for twist knots
- Superintegrability of Kontsevich matrix model
- On rectangular HOMFLY for twist knots
- Differential expansion for link polynomials
- Extension of KNTZ trick to non-rectangular representations
- On Factorization of Generalized Macdonald Polynomials
- On exclusive Racah matrices for rectangular representations
- Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structure
- The non-commutative -polynomial of twist knots
- Evolution properties of the knot's defect
- Overview of knot invariants at roots of unity