HOMFLY for twist knots and exclusive Racah matrices in representation [333]

Abstract

Next step is reported in the program of Racah matrices extraction from the differential expansion of HOMFLY polynomials for twist knots: from the double-column rectangular representations R=[rr] to a triple-column and triple-hook R=[333]. The main new phenomenon is the deviation of the particular coefficient $f_{[332]}^{[21]}$ from the corresponding skew dimension, what opens a way to further generalizations.

10 pages

References in corpus (8)

• HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
• Differential expansion and rectangular HOMFLY for the figure eight knot
• On rectangular HOMFLY for twist knots
• Differential expansion for link polynomials
• On moduli space of symmetric orthogonal matrices and exclusive Racah matrix $\bar{S}$ for representation $R=[3,1]$ with multiplicities
• Rectangular superpolynomials for the figure-eight knot
• On exclusive Racah matrices $\bar{S}$ for rectangular representations
• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$

Cited by in corpus (7)

• Perspectives of differential expansion
• Knot polynomials for twist satellites
• Extension of KNTZ trick to non-rectangular representations
• On exclusive Racah matrices $\bar{S}$ for rectangular representations
• KNTZ trick from arborescent calculus and the structure of differential expansion
• Cyclotomic expansions of HOMFLY-PT colored by rectangular Young diagrams
• Pentad and triangular structures behind the Racah matrices