Incarnations of XXX slN Bethe ansatz equations and integrable hierarchies
Abstract
We consider the space of solutions of the Bethe ansatz equations of the slN XXX quantum integrable model, associated with the trivial representation of slN. We construct a family of commuting flows on this space and identify the flows with the flows of coherent rational Ruijesenaars-Schneider systems. For that we develop in full generality the spectral transform for the rational Ruijesenaars-Schneider system.
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