On the Links-Gould invariant of links

We introduce and study in detail an invariant of (1, 1) tangles. This invariant, derived from a,family of four dimensional representations of the quantum superalgebra U-q[gl(2/1)], will be referred to as the Links-Could invariant. We find that out invariant is distinct from the Jones, HOMFLY and Kauffman polynomials (detecting chirality of some links where these invariants fail), and that it does not distinguish mutants or inverses. The method of evaluation is based on an abstract tensor state model for the invariant that is quite useful for computation as well as theoretical exploration.