Galois Relations on Knot Invariants

Abstract

We discuss the existence of Galois relations obeyed by certain link invariants. Some of these relations have recently been identified and exploited within the context of CFT and Lie/Kac-Moody representation theory. These relations should aid in computing knot invariants. They probably have an interpretation in terms of quasitriangular (quasi-)Hopf algebras. They could also have a topological interpretation, and may serve as a concrete model for related ideas of Degiovanni, Drinfeld, Grothendieck, Ihara, and others.