Classical and quantum-mechanical systems of Toda lattice type. I

DOI10.1007/BF01213608zbMath0503.22013MaRDI QIDQ1173171

Nolan R. Wallach, Roe Goodman

Publication date: 1982

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

zbMATH Keywords

Laplace operatoruniversal enveloping algebraPoisson algebrageneralised Lie groupsLax formsperiodic and nonperiodic Toda lattices

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Constructive quantum field theory (81T08) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Miscellaneous applications of functional analysis (46N99)

Related Items (18)

Nonlinear equations and graded Lie algebras ⋮ Symmetries, conserved quantities, and hierarchies for some lattice systems with soliton structure ⋮ Quantum Toda systems and Lax pairs ⋮ A group approach to the integration of the infinite Toda chain ⋮ Asymptotic expansions of matrix coefficients of Whittaker vectors at irregular singularities ⋮ Quantum cohomology of the infinite-dimensional generalized flag manifolds ⋮ The finite Toda lattices ⋮ On the complete integrability of the periodic quantum Toda lattice ⋮ Quantum integrable systems constrained on the sphere ⋮ The Toda lattice, Dynkin diagrams, singularities and Abelian varieties ⋮ The geometric nature of the Flaschka transformation ⋮ Unitarity of the SoV transform for the Toda chain ⋮ The combinatorial quantum cohomology ring of \(G/B\) ⋮ Classical and quantum mechanical systems of Toda-lattice type. III: Joint eigenfunctions of the quantized systems ⋮ Quantum integrability for the Kovalevsky top ⋮ Higher-Order Sugawara Operators for Affine Lie Algebras ⋮ Integrable Hamiltonians with exponential potential ⋮ Classical and quantum mechanical systems of Toda-lattice type. II: Solutions of the classical flows

Cites Work

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• The solution to a generalized Toda lattice and representation theory
• Completely integrable systems, Euclidean Lie algebras, and curves
• Whittaker vectors and conical vectors
• The spectrum of Jacobi matrices
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• On Whittaker vectors and representation theory
• Representation of Elliptic Operators in an Enveloping Algebra
• Explicit solutions of classical generalized Toda models

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