Links–Gould invariant conjecture for braided exterior algebras

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Let VV be a vector space of dimension NN, let ρ\rho be the RR-matrix-induced structure on the braided exterior algebra [...].[...]. For a long knot, let JρJ_{\rho} denote the associated invariant. Links–Gould invariant conjecture. The invariant has the form

Jρ=LG⁡(N) ⁣(p,t)id⁡Λp(V),J_{\rho}=\operatorname{LG}^{(N)}\!(p,t)\operatorname{id}_{\Lambda_p(V)},

where LG⁡(N) ⁣(p,t)\operatorname{LG}^{(N)}\!(p,t) is the Links–Gould invariant associated with a 2N2^N-dimensional representation of the super quantum group Uq(gl(N∣1))U_q(\mathfrak{gl}(N|1)). The conjecture identifies the invariants arising from these braided exterior-algebra solutions with the Links–Gould invariants; the source gives no resolution beyond the stated formulation.

References

Primary source

Rinat Kashaev and Vladimir Mangazeev, “On braided Hopf structures on exterior algebras”, arXiv:2505.15569 (2025).

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