Unitarity of the SoV transform for the Toda chain

DOI10.1007/s00220-014-2134-6zbMath1308.81088arXiv1306.4967OpenAlexW2001353916MaRDI QIDQ2258000

Karol Kajetan Kozlowski

Publication date: 2 March 2015

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

Full work available at URL: https://arxiv.org/abs/1306.4967

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Inverse scattering problems in quantum theory (81U40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Many-body theory; quantum Hall effect (81V70)

Related Items

Line operators in theories of class \( \mathcal{S} \), quantized moduli space of flat connections, and Toda field theory, Spin chains and Gustafson’s integrals, Unitarity of the SoV transform for \(\mathrm{SL}(2,\mathbb{C})\) spin chains, Basso-Dixon correlators in two-dimensional fishnet CFT, Completeness of SoV representation for \(\mathrm{SL}(2,\mathbb{R})\) spin chains, Aspects of the inverse problem for the Toda chain, On the separation of variables for the modular XXZ magnet and the lattice sinh-Gordon models, Separation of variables for the quantum \(\mathrm{SL} (3, \mathbb{C} )\) spin magnet: eigenfunctions of the Sklyanin \(B\)-operator, On complex gamma-function integrals, Mirror channel eigenvectors of the \(d\)-dimensional fishnets

Cites Work

• Unnamed Item
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• Separation of variables in the Gaudin model
• Whittaker functions on semisimple Lie groups
• On explicit integral formulas for \(\text{GL}(n, \mathbb R)\)-Whittaker functions. With an appendix by Daniel Bump, Solomon Friedberg, and Jeffrey Hoffstein
• Baxter operator and archimedean Hecke algebra
• Complete set of eigenfunctions of the quantum Toda chain
• Classical and quantum mechanical systems of Toda-lattice type. II: Solutions of the classical flows
• The solution to a generalized Toda lattice and representation theory
• Classical and quantum-mechanical systems of Toda lattice type. I
• Classical and quantum mechanical systems of Toda-lattice type. III: Joint eigenfunctions of the quantized systems
• Integral representation for the eigenfunctions of a quantum periodic Toda chain
• Transition function for the Toda chain
• Partition function of the eight-vertex lattice model
• Integral representations for the eigenfunctions of quantum open and periodic Toda chains from the QISM formalism
• Liouville Type Models in the Group Theory Framework: I. Finite-Dimensional Algebras
• Quantization of models with non-compact quantum group symmetry: modular XXZ magnet and lattice sinh-Gordon model
• On a Gauss-Givental representation of quantum Toda chain wave function
• The periodic Toda chain and a matrix generalization of the Bessel function recursion relations
• Some q-Beta and Mellin-Barnes Integrals on Compact Lie Groups and Lie Algebras
• Stationary Phase Integrals, Quantum Toda Lattices, Flag Manifolds and the Mirror Conjecture
• Fonctions de Whittaker associées aux groupes de Chevalley
• Intégrales d'entrelacement et fonctions de Whittaker
• Noncompact Heisenberg spin magnets from high-energy QCD. I: Baxter Q-operator and separation of variables