Integrality of Homfly 1-tangle invariants

Given an invariant J(K) of a knot K, the corresponding 1-tangle invariant J'(K) = J(K)/J(U) is defined as the quotient of J(K) by its value J(U) on the unknot U. We prove here that when J is the Homfly satellite invariant determined by decorating K with any eigenvector of the meridian map in the Homfly skein of the annulus then J' is always an integer 2-variable Laurent polynomial. Specialisation of the 2-variable polynomials for suitable choices of eigenvector shows that the 1-tangle irreducible quantum sl(N) invariants of K are integer 1-variable Laurent polynomials.