Spectrum and orthogonality of the Bethe ansatz for the periodic \(q\)-difference Toda chain on \(\mathbb{Z}_{m+1}\)

DOI10.1007/s00023-023-01265-6OpenAlexW4313830828MaRDI QIDQ6045747

Jan Felipe van Diejen

Publication date: 12 May 2023

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00023-023-01265-6

zbMATH Keywords

Lieb-Liniger modelBethe Ansatz\(q\)-difference Toda chainToda correspondenceYang-Yang type Morse functions

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Exactly solvable models; Bethe ansatz (82B23) Difference equations, scaling ((q)-differences) (39A13) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Lattice dynamics; integrable lattice equations (37K60) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Special quantum systems, such as solvable systems (81Q80)

Cites Work

• On \(q\)-deformed \(\mathfrak{gl}_{\ell+1}\)-Whittaker function. III
• Fermionic formulas for eigenfunctions of the difference Toda Hamiltonian
• Diagonalization of an integrable discretization of the repulsive delta Bose gas on the circle
• Quantum inverse scattering method for the \(q\)-boson model and symmetric functions
• Quantum relativistic Toda chains
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• Correlation functions for a strongly correlated boson system
• Exact quantization conditions for the relativistic Toda lattice
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• Integrable boundary interactions for Ruijsenaars' difference Toda chain
• Affine Pieri rule for periodic Macdonald spherical functions and fusion rings
• Macdonald processes
• Relativistic Toda systems
• Kernel functions and Bäcklund transformations for relativistic Calogero-Moser and Toda systems
• q-bosons, Toda lattice, Pieri rules and Baxterq-operator
• The periodic relativistic Toda lattice: direct and inverse problem
• A q-difference Baxter operator for the Ablowitz–Ladik chain
• A path model for Whittaker vectors
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