Extension of KNTZ trick to non-rectangular representations

Abstract

We claim that the recently discovered universal-matrix precursor for the $F$ functions, which define the differential expansion of colored polynomials for twist and double braid knots, can be extended from rectangular to non-rectangular representations. This case is far more interesting, because it involves multiplicities and associated mysterious gauge invariance of arborescent calculus. In this paper we make the very first step -- reformulate in this form the previously known formulas for the simplest non-rectangular representations [r,1] and demonstrate their drastic simplification after this reformulation.

arXiv comment6 pages

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Cited by in corpus (12)

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• Distinguishing Mutant Knots
• Perspectives of differential expansion
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• Defect and degree of the Alexander polynomial
• Evolution properties of the knot's defect