Abstract
The spectral problem for an integrable system of particles satisfying the fusion rules of is expressed in terms of exact inversion identities satisfied by the commuting transfer matrices of the integrable fused interaction round a face model of Jimbo, Miwa and Okado. The identities are proven using local properties of the Boltzmann weights, in particular the Yang–Baxter equation and unitarity. They are closely related to the consistency conditions for the construction of eigenvalues obtained in the separation of variables approach to integrable vertex models.
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