Other quantum relatives of the Alexander polynomial through the Links-Gould invariants

Kohli, Ben-Michael; Patureau-Mirand, Bertrand

doi:10.1090/proc/13699

Other quantum relatives of the Alexander polynomial through the Links-Gould invariants
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by Ben-Michael Kohli and Bertrand Patureau-Mirand PDF

Proc. Amer. Math. Soc. 145 (2017), 5419-5433 Request permission

Abstract:

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 $U_q{\mathfrak {sl}(2)}$ at fourth roots of unity, or by considering the super Hopf algebra $U_q\mathfrak {gl}(1|1)$. In this paper, we show these Hopf algebras share properties with the $-1$ specialization of $U_q\mathfrak {gl}(n|1)$ leading to the proof of a conjecture by David De Wit, Atsushi Ishii and Jon Links on the Links-Gould invariants.

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