On the Links-Gould invariant and the square of the Alexander polynomial

TL;DR

This paper establishes a relationship between the Links-Gould invariants and powers of the Alexander-Conway polynomial, revealing that certain specialized Links-Gould polynomials derive from exterior powers of Burau representations.

Contribution

It demonstrates a novel connection between the Links-Gould invariants and the Alexander polynomial through representation theory and braid group analysis.

Findings

Links-Gould invariants relate to powers of the Alexander-Conway polynomial.

Specialized Links-Gould polynomials derive from exterior powers of Burau representations.

The paper provides formulas linking these invariants and polynomials.

Abstract

This paper gives a connection between well chosen reductions of the Links-Gould invariants of oriented links and powers of the Alexander-Conway polynomial. We prove these formulas by showing the representations of the braid groups we derive the specialized Links-Gould polynomials from can be seen as exterior powers of copies of Burau representations.