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Quantum relativistic Toda chain. (English) Zbl 1109.82317

Summary: Investigated is the quantum relativistic periodic Toda chain, to each site of which the ultra-local Weyl algebra is associated. Weyl’s \(q\) we are considering here is restricted to be inside the unit circle. Quantum Lax operators of the model are intertwined by six-vertex \(R\)-matrix. Both independent Baxter’s \(Q\)-operators are constructed explicitly.

MSC:

82B23 Exactly solvable models; Bethe ansatz
37K60 Lattice dynamics; integrable lattice equations
81R12 Groups and algebras in quantum theory and relations with integrable systems
82B10 Quantum equilibrium statistical mechanics (general)
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