Hidden symmetry of the quantum Calogero-Moser system

DOI10.1016/0375-9601(96)00421-5zbMath0972.39503arXivsolv-int/9509001OpenAlexW3121529539MaRDI QIDQ1967920

Vadim B. Kuznetsov

Publication date: 7 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9509001

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Many-body theory; quantum Hall effect (81V70) Difference operators (39A70)

Related Items (20)

Nonlinear supersymmetry in the quantum Calogero model ⋮ Degenerate integrability of quantum spin Calogero-Moser systems ⋮ Integrable and superintegrable extensions of the rational Calogero–Moser model in three dimensions ⋮ The tetrahexahedric angular Calogero model ⋮ The quantum harmonic oscillator on the sphere and the hyperbolic plane ⋮ On a second Lax structure for the Calogero-Moser system: time-dependent constants and superintegrability ⋮ Algebra of Dunkl Laplace-Runge-Lenz vector ⋮ The structure of invariants in conformal mechanics ⋮ On the superintegrability of the rational Ruijsenaars-Schneider model ⋮ A Casimir operator for a Calogero W algebra ⋮ Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model ⋮ A note on superintegrability of the quantum Calogero model. ⋮ Nonlinear symmetries of perfectly invisible \textit{PT}-regularized conformal and superconformal mechanics systems ⋮ Quadratic algebra associated with rational Calogero-Moser models ⋮ Superintegrability of the Calogero–Moser system: Constants of motion, master symmetries, and time-dependent symmetries ⋮ Integrability, intertwiners and non-linear algebras in Calogero models ⋮ New superintegrable models on spaces of constant curvature ⋮ The role of commuting operators in quantum superintegrable systems ⋮ Master integrals, superintegrability and quadratic algebras ⋮ A superintegrable model with reflections onSⁿ⁻¹and the higher rank Bannai–Ito algebra

Cites Work

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• An uncertainty principle for integral operators
• Commutative rings of partial differential operators and Lie algebras
• An elementary approach to the hypergeometric shift operators of Opdam
• Differential-Difference Operators Associated to Reflection Groups
• The Quantum Calogero-Moser Model: Algebraic Structures

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