Adler–Kostant–Symes scheme for face and Calogero–Moser–Sutherland-type models

DOI10.1063/1.532453zbMath0976.81016arXivsolv-int/9710006OpenAlexW1583891631MaRDI QIDQ4701603

Branislav Jurčo, Peter Schupp

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9710006

zbMATH Keywords

IRF modelselliptic quantum groupsface Hopf algebrasquantum Lax equations

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) PDEs in connection with quantum mechanics (35Q40) Exactly solvable models; Bethe ansatz (82B23) Many-body theory; quantum Hall effect (81V70) Groups and algebras in quantum theory and relations with integrable systems (81R12) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20)

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Cites Work

• Solvable lattice models whose states are dominant integral weights of \(A^{(1)}_{n-1}\)
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• The solution to a generalized Toda lattice and representation theory
• Systems of Toda type, inverse spectral problems, and representation theory
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Elliptic quantum groups and Ruijsenaars models
• Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups
• Quantum group symmetry of partition functions of IRF models and its application to Jones' index theory
• Quantized Lax equations and their solutions
• Ruijsenaars' commuting difference operators as commuting transfer matrices
• Macdonald's polynomials and representations of quantum groups
• Compact quantum groups of face type
• The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
• A coassociative \(C^*\)-quantum group with nonintegral dimensions
• Twisted Quantum Lax Equations
• Integrability of difference Calogero–Moser systems
• \(R\)-matrix quantization of the elliptic Ruijsenaars-Schneider model

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