  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.
