Commuting difference operators arising from the elliptic C2(1)-face model

DOI10.1063/1.532986zbMath1041.82506arXivmath/9810062OpenAlexW1658601803MaRDI QIDQ4270444

Takeshi Ikeda, Tetsuya Kikuchi, Kohji Hasegawa

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/math/9810062

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Exactly solvable models; Bethe ansatz (82B23) Difference operators (39A70) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (6)

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 ⋮ 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

• Infinite-dimensional Lie algebras, theta functions and modular forms
• Solvable lattice models related to the vector representation of classical simple Lie algebras
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Completely \(\mathbb{Z}\) symmetric \(R\) matrix
• Elliptic quantum groups and Ruijsenaars models
• Elliptic K-matrix associated with Belavin's symmetric R-matrix
• Ruijsenaars' commuting difference operators as commuting transfer matrices
• Dynamical symmetry of integrable quantum systems
• Double affine Hecke algebras and Macdonald's conjectures
• NOTES ON OPERATOR-VALUED SOLUTIONS OF THE YANG-BAXTER EQUATION AND THE REFLECTION EQUATION
• Quantum integrability of the generalized elliptic Ruijsenaars models
• Crossing symmetry in elliptic solutions of the Yang-Baxter equation and a new L-operator for Belavin's solution
• Integrability of difference Calogero–Moser systems
• L-operator for Belavin’s R-matrix acting on the space of theta functions
• Conserved operators of the generalized elliptic Ruijsenaars models
• Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. I: Some fundamental eigenvectors.

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