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In this paper we analyze the classical XXZ spin chain with reflectingboundaries. We exhibit a system of log-canonical coordinates on the phase spacegeneralizing Sklyanin's separation of variables for the periodic XXZ chain, anduse these coordinates to construct action-angle variables for the system. Wealso integrate the flows of the reflection Hamiltonians explicitly in terms ofRiemann theta functions. Central to our analysis is the algebraic integrabilityof the model.

Algebraic integrability of the classical XXZ spin chain with reflecting boundary conditions