Invariants of knots and links at roots of unity

Abstract

We present a comprehensive classification of invariants of knots and links associated with irreducible representations of \uqslN{}, when the parameter of quantization $q$ is a root of unity. We demonstrate that, besides the standard HOMFLY-PT invariants, which are associated with representations with highest and lowest weights, non-trivial invariants can be associated only with nilpotent representations with parameters. We define the corresponding invariants and discuss their relations with standard invariants at particular values of parameters.

26 pages, 12 figures

References in corpus (5)

• Eigenvalue hypothesis for Racah matrices and HOMFLY polynomials for 3-strand knots in any symmetric and antisymmetric representations
• Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants
• Wall Crossing Invariants: from quantum mechanics to knots
• Differential expansion for link polynomials
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Cited by in corpus (2)

• Defect and degree of the Alexander polynomial
• Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalism