Conserved operators of the generalized elliptic Ruijsenaars models

DOI10.1063/1.532622zbMath0986.81122OpenAlexW2083535169MaRDI QIDQ4701550

Yasushi Komori, Kazuhiro Hikami

Publication date: 21 November 1999

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

Full work available at URL: https://doi.org/10.1063/1.532622

zbMATH Keywords

Yang-Baxter equationreflection equationintegrable families

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Many-body theory; quantum Hall effect (81V70)

Related Items (10)

Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry ⋮ Commuting difference operators arising from the elliptic C2(1)-face model ⋮ Elliptic Racah polynomials ⋮ Eigenvalues of Ruijsenaars–Schneider models associated with An−1 root system in Bethe ansatz formalism ⋮ ON THE INTEGRABILITY OF CLASSICAL RUIJSENAARS–SCHNEIDER MODEL OF BC₂ TYPE ⋮ Scattering theory of the hyperbolic \(BC_n\) Sutherland and the rational \(BC_n\) Ruijsenaars-Schneider-Van Diejen models ⋮ Integrability of the Cn and BCn Ruijsenaars–Schneider models ⋮ The Lax pairs for elliptic Cn and BCn Ruijsenaars–Schneider models and their spectral curves ⋮ Ruijsenaars’ commuting difference operators and invariant subspace spanned by theta functions ⋮ Essential self-adjointness of the elliptic Ruijsenaars models

Cites Work

• Factorizing particles on a half-line and root systems
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Completely \(\mathbb{Z}\) symmetric \(R\) matrix
• Ruijsenaars' commuting difference operators as commuting transfer matrices
• Separation of variables for the Ruijsenaars system
• Elliptic Dunkl operators, root systems, and functional equations
• Elliptic quantum many-body problem and double affine Knizhnik- Zamolodchikov equation
• Simple construction of the elliptic boundary \(K\)-matrix
• Integrability, Fusion, and Duality in the Elliptic Ruijsenaars Model
• Quantum integrability of the generalized elliptic Ruijsenaars models
• Integrability of difference Calogero–Moser systems
• Affine Hecke algebra, Macdonald polynomials, and quantum many-body systems
• Dynamicalr-matrix for the elliptic Ruijsenaars - Schneider system
• BoundaryK-matrix, elliptic Dunkl operator and quantum many-body systems
• Boundary conditions for integrable quantum systems
• Difference Calogero–Moser systems and finite Toda chains
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