Incarnations of XXX \widehat\fraksl_N Bethe ansatz equations and integrable hierarchies

2019/07/29 by I. M. Krichever, Krichever, Igor, Alexander Varchenko +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1907.12198

openalex publication_date 2019/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the space of solutions of the Bethe ansatz equations of the \widehat\fraksl_N XXX quantum integrable model, associated with the trivial representation of \widehat\fraksl_N. 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.

Citations

• Critical points of master functions and the mKdV hierarchy of type A²₂
• Populations of solutions of the XXX Bethe equations associated to Kac-Moody algebras

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