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 LG^{m,n}, based on quantum R matrices associated with the (\dot{0}_m | \dotα_n) representations of the quantum superalgebras U_q[gl(m|n)]. Explicit details of the state models for the cases n=1 and m=1,2,3,4 are supplied. Some evaluations of the new link invariants are provided, as are some of their gross properties.