Invariants of knots and links at roots of unity

We present a comprehensive classification of invariants of knots and links associated with irreducible representations of Uq(slN), when the parameter of quantization q is a root of unity. We demonstrate that, besides the standard colored 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. While such invariants were discussed for Uq(sl2) and are known as the ADO invariants, we generalize them to the general Uq(slN) case and discuss their relations with standard invariants at particular values of parameters. (c) 2022 Elsevier B.V. All rights reserved.