An Infinite Suite of Links–Gould Invariants

Abstract

This paper describes a method to obtain state model parameters for an infinite series of Links–Gould link invariants LGm,n, based on quantum R matrices associated with the [Formula: see text] representations of the quantum superalgebras Uq[gl(m|n)]. Explicit details of the state models for the cases n=1 and m=1, 2, 3, 4 are supplied. Some gross properties of the link invariants are provided, as well as some explicit evaluations.