Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems

DOI10.1007/BF02066651zbMath0855.58039arXivhep-th/9412116MaRDI QIDQ1920649

Anton V. Zabrodin

Publication date: 11 February 1997

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9412116

zbMATH Keywords

quantum inverse scatteringAzbel-Hofstadter problem

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Inverse scattering problems in quantum theory (81U40) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

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Cites Work

• Unnamed Item
• Group theory approach to scattering
• Some algebraic structures connected with the Yang-Baxter equation. Representations of quantum algebras
• Irreducible representations of the quantum analogue of SU(2)
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Poisson manifolds and the Schouten bracket
• Quantum dressing orbits on compact groups
• Quasi-exactly-solvable problems and sl(2) algebra
• Generalized Bethe ansatz equations for Hofstadter problem
• Algebraization of difference eigenvalue equations related to \(U_q(\text{sl}_2)\)
• Quantum group and magnetic translations Bethe ansatz for the Asbel-Hofstadter problem
• Chiral Potts model as a descendant of the six-vertex model
• Algebraic structures related to reflection equations
• A new basis for the representations of the rotation group. Lamé and Heun polynomials
• Askey–Wilson Polynomials as Zonal Spherical Functions on the ${\operatorname{SU}}(2)$ Quantum Group