GLZ invariant conjecture for the Alexander polynomial

Let LL be an oriented link, let nn be a positive integer, let GLZLn(τ,t)GLZ^n_L(\tau,t) denote the invariant associated with the quantum superalgebra Uq[osp(22n)]U_q[\operatorname{osp}(2|2n)], and let ΔL\Delta_L denote the Alexander polynomial. GLZ conjecture.

GLZLn(τ,eπ1/2)=ΔL(τ4)n.GLZ^n_L(\tau,e^{\pi\sqrt{-1}/2})=\Delta_L(\tau^4)^n.

The conjecture is presented as an analogue of the preceding generalised Links–Gould relation. Its resolution is not indicated in the supplied text.

Sources & referencesView supporting material

Primary source

David De Wit, Atsushi Ishii and Jon Links, “Infinitely many two-variable generalisations of the Alexander-Conway polynomial”, arXiv:math/0405403 (2005).

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