Elliptic quantum groups and Ruijsenaars models

DOI10.1007/BF02764216zbMath0924.17011arXivq-alg/9704005OpenAlexW3100355303MaRDI QIDQ1284947

Giovanni Felder, Alexander Varchenko

Publication date: 9 November 1999

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

Full work available at URL: https://arxiv.org/abs/q-alg/9704005

zbMATH Keywords

deformationYang-Baxter equationvector representationelliptic quantum groupdynamical \(R\)-matricesRuijsenaars operators

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)

Related Items

Construction of eigenfunctions for the elliptic Ruijsenaars difference operators, Commuting difference operators arising from the elliptic C2(1)-face model, Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess-Zumino-Witten fusion rings, Algebraic Bethe ansatz for the elliptic quantum group \(E_{\tau,\eta}(sl_n)\) and its applications, Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and \(R\)-matrix identities, Branes and integrable lattice models, Explicit solution of the (quantum) elliptic Calogero-Sutherland model, Surface defects and elliptic quantum groups, Hilbert space theory for reflectionless relativistic potentials, Ruijsenaars’ commuting difference operators and invariant subspace spanned by theta functions, Essential self-adjointness of the elliptic Ruijsenaars models, Adler–Kostant–Symes scheme for face and Calogero–Moser–Sutherland-type models, Representations of the elliptic affine Hecke algebras, The elliptic \(\text{GL}(n)\) dynamical quantum group as an \(\mathfrak h\)-Hopf algebroid, Traces of intertwiners for quantum groups and difference equations. I, Lax equations for relativistic GL(NM,C) Gaudin models on elliptic curve

Cites Work

• On representations of the elliptic quantum group \(E_ \tau,\eta(sl_ 2)\)
• Elliptic curves and soliton matrix differential equations
• The \(A_ n^{(1)}\) face models
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Yang-Baxter equation and representation theory. I
• Algebraic integrability of the two-body Ruijsenaars operator
• Ruijsenaars' commuting difference operators as commuting transfer matrices
• Algebraic Bethe ansatz for the elliptic quantum group \(E_{\tau,\eta} (sl_2\))
• Macdonald's polynomials and representations of quantum groups
• The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
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