OTHER QUANTUM RELATIVES OF THE ALEXANDER POLYNOMIAL THROUGH THE LINKS-GOULD INVARIANTS

In 2006, Oleg Viro studied two interpretations of the (multivariable) Alexander polynomial understood as a quantum link invariant: either by considering the quasitriangular Hopf algebra associated to U(q)sl(2) at fourth roots of unity, or by considering the super Hopf algebra U(q)gl(1 vertical bar 1). In this paper, we show these Hopf algebras share properties with the -1 specialization of U(q)gl(n vertical bar 1) leading to the proof of a conjecture by David De Wit, Atsushi Ishii and Jon Links on the Links-Gould invariants.