  We present a new conjectural symmetry of the colored Alexander polynomial,
that is the specialization of the quantum $\mathfrak{sl}_N$ invariant widely
known as the colored HOMFLY-PT polynomial. We provide arguments in support of
the existence of the symmetry by studying the loop expansion and the character
expansion of the colored HOMFLY-PT polynomial. We study the constraints this
symmetry imposes on the group theoretic structure of the loop expansion and
provide solutions to those constraints. The symmetry is a powerful tool for
research on polynomial knot invariants and in the end we suggest several
possible applications of the symmetry.
