Matrix integral expansion of colored Jones polynomials for figure-eight knot
arXiv:1411.5698 · doi:10.1134/S0021364015010026
Abstract
In this note we examine a possible extension of the matrix integral representation of knot invariants beyond the class of torus knots. In particular, we study a representation of the SU(2) quantum Racah coefficients by double matrix integrals. We find that the Racah coefficients are mapped to expansion coefficients in some basis of double integrals. The transformed coefficients have a number of interesting algebraic properties.
arXiv comment5 pages, 7 figures
References in corpus (13)
- Torus knots and mirror symmetry
- HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
- On Link Invariants and Topological String Amplitudes
- Three Dimensional Chern-Simons Theory as a Theory of Knots and Links
- On KP-integrable Hurwitz functions
- Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid
- 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
- Racah coefficients and extended HOMFLY polynomials for all 5-, 6- and 7-strand braids
- Colored HOMFLY polynomials as multiple sums over paths or standard Young tableaux
- Multiplicity-free quantum 6j-symbols for U_q(sl_N)
- Towards matrix model representation of HOMFLY polynomials
- A formula for the HOMFLY polynomial of rational links