Hilbert-Schmidt operators vs. integrable systems of elliptic Calogero-Moser type. I: The eigenfunction identities

DOI10.1007/s00220-008-0707-yzbMath1180.37097OpenAlexW2027412941MaRDI QIDQ842418

Simon N. M. Ruijsenaars

Publication date: 25 September 2009

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

Full work available at URL: https://doi.org/10.1007/s00220-008-0707-y

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items (17)

Construction of eigenfunctions for the elliptic Ruijsenaars difference operators ⋮ Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry ⋮ Hilbert-Schmidt operators vs. Integrable systems of elliptic Calogero-Moser type. II: The \(A _{N - 1}\) case: First steps ⋮ Difference operators of Sklyanin and van Diejen type. ⋮ Dynamical correlation functions and finite-size scaling in the Ruijsenaars-Schneider model ⋮ Ground state wavefunctions of elliptic relativistic integrable Hamiltonians ⋮ On positive Hilbert-Schmidt operators ⋮ Self-duality of the compactified Ruijsenaars-Schneider system from quasi-Hamiltonian reduction ⋮ Non-stationary Ruijsenaars functions for \(\kappa = t^{-1/N}\) and intertwining operators of Ding-Iohara-Miki algebra ⋮ Basic properties of non-stationary Ruijsenaars functions ⋮ On Barnes' multiple zeta and gamma functions ⋮ A relativistic hypergeometric function ⋮ Source identity and kernel functions for elliptic Calogero-Sutherland type systems ⋮ Source identities and kernel functions for the deformed Koornwinder-van Diejen models ⋮ Zero-eigenvalue eigenfunctions for differences of elliptic relativistic Calogero-Moser hamiltonians ⋮ Source identity and kernel functions for Inozemtsev-type systems ⋮ Eigenfunctions of the van Diejen model generated by gauge and integral transformations

Cites Work

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• Hilbert-Schmidt operators vs. Integrable systems of elliptic Calogero-Moser type. II: The \(A _{N - 1}\) case: First steps
• Hilbert-Schmidt operators vs. integrable systems of elliptic Calogero-Moser type III: The Heun case
• Zero-eigenvalue eigenfunctions for differences of elliptic relativistic Calogero-Moser hamiltonians
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Commuting families of symmetric differential operators
• Lax representation with spectral parameter on a torus for integrable particle systems
• Hilbert-Schmidt operators vs. integrable systems of elliptic Calogero-Moser type IV. The relativistic Heun (van Diejen) case
• Quantum integrability of the generalized elliptic Ruijsenaars models
• Integrability of difference Calogero–Moser systems
• First order analytic difference equations and integrable quantum systems
• Anyons and the elliptic Calogero-Sutherland model

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