Quantum integrable systems and representations of Lie algebras

DOI10.1063/1.531056zbMath0861.17002arXivhep-th/9311132OpenAlexW2051873484MaRDI QIDQ4873300

Pavel I. Etingof

Publication date: 14 May 1997

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

Full work available at URL: https://arxiv.org/abs/hep-th/9311132

zbMATH Keywords

Hamiltoniansquantum many-body problemquantum integralsSutherland operatorcompletely integrable quantum systemimages of higher CasimirOlshanetsky-Perelomov theorem

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

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Cites Work

• Integrable systems with Delta-potential
• Sugawara operators and Kac-Kazhdan conjecture
• Singular vectors in Verma modules over affine algebras
• Representations of affine Lie algebras, parabolic differential equations, and Lamé functions
• Integrability in the theory of Schrödinger operator and harmonic analysis
• AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS

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