How quantum groups encode knot invariants across all gauge groups

A-polynomials are algebraic constraints that encode topological information about knots and appear naturally in 3d gauge theory. The authors develop a systematic way to generalize these polynomials from $SU(2)$ to arbitrary $SU(N)$ using Clebsch-Gordan decompositions and huge representations of quantum groups. This opens a path to computing knot invariants for richer gauge theories and arbitrary Lie algebras.