Difference of mutant knot invariants and their differential expansion

Abstract

We evaluate the differences of HOMFLY-PT invariants for pairs of mutant knots colored with representations of $SL(N)$, which are large enough to distinguish between them. These mutant pairs include the pretzel mutants, which require at least the representation, labeled by the Young diagram $[4,2]$. We discuss the differential expansion for the differences, it is non-trivial in the case of mutants, which have the non-zero defect. The most effective technical tool, in this case, turns out to be the standard Reshetikhin-Turaev approach.

6 pages

References in corpus (4)

• HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
• Differential expansion for link polynomials
• Mutant knots with symmetry
• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$