Multivariable link invariants arising from [formula omitted] and the Alexander polynomial

Abstract

In this paper we construct a multivariable link invariant arising from the quantum group associated with the special linear Lie superalgebra s l ( 2 | 1 ) . The usual quantum group invariant of links associated with (generic) representations of s l ( 2 | 1 ) is trivial. However, we modify this construction and define a non-trivial link invariant. This new invariant can be thought of as a multivariable version of the Links–Gould invariant. We also show that after a variable reduction our invariant specializes to the Conway potential function, which is a refinement of the multivariable Alexander polynomial.