Duality for Knizhnik-Zamolodchikov and dynamical operators

DOI10.3842/SIGMA.2020.035zbMath1487.17035arXiv1904.07309OpenAlexW2936589035MaRDI QIDQ2176564

Filipp Uvarov, Vitaly O. Tarasov

Publication date: 5 May 2020

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.07309

zbMATH Keywords

\mathfrak{gl}_n)\)-dualitydynamical operatorsKnizhnik-Zamolodchikov operatorsthe \((\mathfrak{gl}_k

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) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Discrete version of topics in analysis (39A12) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (3)

Duality for Bethe algebras acting on polynomials in anticommuting variables ⋮ Dualities in quantum integrable many-body systems and integrable probabilities. I. ⋮ Difference operators and duality for trigonometric Gaudin and dynamical Hamiltonians

Cites Work

• The trigonometric Casimir connection of a simple Lie algebra
• Differential equations compatible with KZ equations
• Dynamical Weyl groups and applications
• \((\mathfrak{gl}_M, \mathfrak{gl}_N)\)-dualities in Gaudin models with irregular singularities
• Dynamical differential equations compatible with rational qKZ equations
• Duality for Knizhnik-Zamolodchikov and dynamical equations
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