GLZ invariant conjecture for the Alexander polynomial

About 22 years old · traced to

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⁡(2∣2n)]U_q[\operatorname{osp}(2|2n)], and let ΔL\Delta_L denote the Alexander polynomial. GLZ conjecture.

GLZLn(τ,eπ−1/2)=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.

References

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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