An infinite suite of Links-Gould invariants

This paper describes a method to obtain state model parameters for an infin ite series of Links-Gould link invariants LG(m,n), based on quantum R matri ces associated with the ((0) over dot(m) / (alpha) over dot(n)) representat ions of the quantum superalgebras Uq[gl(m/n)]. Explicit details of the stat e models for the cases n = 1 and m = 1,2,3,4 are supplied. Some gross prope rties of the link invariants are provided, as well as some explicit evaluat ions.