QKZ-Ruijsenaars correspondence revisited

DOI10.1016/j.nuclphysb.2017.06.025zbMath1373.81245arXiv1704.04527OpenAlexW2605813591MaRDI QIDQ2412771

Yanyan Li

Publication date: 27 October 2017

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.04527

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) Many-body theory; quantum Hall effect (81V70) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Difference equations, scaling ((q)-differences) (39A13)

Related Items

Poisson-Lie analogues of spin Sutherland models, Generalized devil's staircase and RG flows, Supersymmetric extension of qKZ-Ruijsenaars correspondence, Dualities in quantum integrable many-body systems and integrable probabilities. I., Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary

Cites Work

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• Trigonometric version of quantum-classical duality in integrable systems
• Spectrum of quantum transfer matrices via classical many-body systems
• BPS states in the \(\Omega\)-background and torus knots
• A solution to quantum Knizhnik-Zamolodchikov equations and its application to eigenvalue problems of the Macdonald type
• Classical tau-function for quantum spin chains
• A new class of integrable systems and its relation to solitons
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Quantum affine algebras and holonomic difference equations
• Integrable connections related to zonal spherical functions
• Shift operators for the quantum Calogero-Sutherland problems via Knizhnik-Zamolodchikov equation
• Integration of quantum many-body problems by affine Knizhnik- Zamolodchikov equations
• \(R\)-matrix arising from affine Hecke algebras and its application to Macdonald's difference operators
• Ruijsenaars' commuting difference operators as commuting transfer matrices
• Supersymmetric quantum spin chains and classical integrable systems
• Quantum Spin Chains and Integrable Many-Body Systems of Classical Mechanics
• Quantum Affine Knizhnik-Zamolodchikov Equations and Quantum Spherical Functions, I
• KZ-Calogero correspondence revisited