Integrable Systems, Shuffle Algebras, and Bethe Equations

DOI10.1090/mosc/259zbMath1416.17017OpenAlexW2559001267MaRDI QIDQ2973038

Boris L. Feigin

Publication date: 31 March 2017

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/mosc/259

zbMATH Keywords

quantum groupintegrable systemaffine Lie algebrashuffle algebracenter at the critical levelBethe equationsDrinfeld-Sokolov reduction

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Vertex operators; vertex operator algebras and related structures (17B69) Exactly solvable models; Bethe ansatz (82B23) Applications of Lie algebras and superalgebras to integrable systems (17B80) Ring-theoretic aspects of quantum groups (16T20)

Related Items

TOROIDAL q-OPERS, Matrix divisors on Riemann surfaces and Lax operator algebras, Quantum loop groups and shuffle algebras via Lyndon words

Cites Work

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• Double ramification cycles and quantum integrable systems
• Bethe subalgebras of \(U_q(\widehat{\mathfrak{gl}}_n)\) via shuffle algebras
• The affine Yangian of \(\mathfrak{gl}_1\) revisited
• Representations of quantum toroidal \(\mathfrak{gl}_n\)
• Quantization of the Drinfel'd-Sokolov reduction.
• Central extensions of quantum current groups
• On spectrum of ILW hierarchy in conformal field theory
• Bethe algebra of homogeneous \(XXX\) Heisenberg model has simple spectrum
• Quantum cohomology of the Hilbert scheme of points in the plane
• The argument shift method and the Gaudin model
• Quantum inverse problem method. I
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Infinite conformal symmetry in two-dimensional quantum field theory
• Orbits of the group of diffeomorphisms of a circle and local Lie superalgebras
• Integrable structure of conformal field theory. II: \(Q\)-operator and DDV equation
• Deformations of \(W\)-algebras associated to simple Lie algebras
• Quantum lattice KdV equation
• Generalization of Drinfeld quantum affine algebras
• Poisson-Lie group of pseudodifferential symbols
• Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz
• Quantization of Lie bialgebras. I
• A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions
• Quantum affine algebras and deformations of the Virasoro and \({\mathcal W}\)-algebras
• Finite type modules and Bethe ansatz for quantum toroidal \(\mathfrak{gl}_1\)
• The quantum Gaudin system
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Quantization of soliton systems and Langlands duality
• A (q,γ) analog of the W1+∞ algebra
• A commutative algebra on degenerate CP1 and Macdonald polynomials
• ON SEPARATION OF VARIABLES AND COMPLETENESS OF THE BETHE ANSATZ FOR QUANTUM _N GAUDIN MODEL
• The semi-infinite homology of Kac-Moody and Virasoro Lie algebras
• ASYMPTOTIC BEHAVIOUR OF THE RESOLVENT OF STURM-LIOUVILLE EQUATIONS AND THE ALGEBRA OF THE KORTEWEG-DE VRIES EQUATIONS
• AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS
• Quantum toroidal $\mathfrak{g}{{\mathfrak{l}}_{1}}$ and Bethe ansatz
• Quantum groups and quantum cohomology