Wrapping construction at the deformed elliptic level

Determine whether the two deformed elliptic long-range spin-chain landscapes—namely, the face-type q-deformed Inozemtsev chain built from Felder’s dynamical R-matrix and the vertex-type Matushko–Zotov (MZ′) chain built from Baxter’s eight-vertex R-matrix—can be constructed by a wrapping procedure analogous to the undeformed periodic/antiperiodic wrapping from the rational Haldane–Shastry chain, and specify the precise mechanism if such a construction exists.

Background

The paper shows that at the undeformed level both the Inozemtsev chain (periodic wrapping) and the SZ′ chain (antiperiodic wrapping) can be built from the rational Haldane–Shastry chain by appropriate wrapping procedures. It highlights that, at the deformed elliptic level, boundary conditions persist in suitably q-deformed and twisted forms.

However, the authors point out that it is unclear whether an analogous wrapping framework exists for the deformed elliptic landscapes (face-type and vertex-type) and, if so, how it should be implemented. Clarifying this would unify construction methods across levels and may shed light on integrability and boundary phenomena in the deformed setting.