An Infinite Suite of Links-Gould Invariants

2000/04/30 by David De Wit · 2 citations
Mathematics · #math.GT #math.QA #msc:57M25 #msc:17B37

paper · pdf

published as Journal of Knot Theory and its Ramifications 10(1):(February 2001) 37-62 · 26 pages, 5 figures. This version adds background material on quantum superalgebras. David De Wit: <http://www.kurims.kyoto-u.ac.jp/~ddw/>

arxiv created 2000/07/09 · arxiv updated 2009/11/30

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 (0_m | α_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.

Cited by

• On some log-concavity properties of the Alexander-Conway and Links-Gould invariants
• On braided Hopf structures on exterior algebras

Related

• The Links-Gould Invariant
• State sums for some super quantum link invariants
• Link Invariants Associated with Gauge Equivalent Solutions of the Yang-Baxter Equation: the One-Parameter Family of Minimal Typical Representations of U_q[gl(2|1)]
• Matrix factorizations and gl(m|k)-quantum invariants
• A universal R-matrix for the quantization of the Lie superalgebra D(2,1,x) and an associated link invariant