Source identities and kernel functions for deformed (quantum) Ruijsenaars models

DOI10.1007/s11005-014-0690-5zbMath1303.81071arXiv1311.4433OpenAlexW3103151580MaRDI QIDQ405619

Edwin Langmann, Farrokh Atai, Martin A. Hallnäs

Publication date: 5 September 2014

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

Full work available at URL: https://arxiv.org/abs/1311.4433

zbMATH Keywords

exactly solvable modelsChalykh-Feigin-Veselov-Sergeev type deformationkernel functionsRuijsenaars models

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Formal methods and deformations in algebraic geometry (14D15) Kernel functions in one complex variable and applications (30C40) Functional identities (associative rings and algebras) (16R60) Special quantum systems, such as solvable systems (81Q80)

Related Items

Higher order deformed elliptic Ruijsenaars operators ⋮ On R-matrix identities related to elliptic anisotropic spin Ruijsenaars-Macdonald operators ⋮ Super-Macdonald polynomials: orthogonality and Hilbert space interpretation ⋮ From Kajihara's transformation formula to deformed Macdonald-Ruijsenaars and Noumi-Sano operators ⋮ Source identities and kernel functions for the deformed Koornwinder-van Diejen models ⋮ Eigenfunctions of the van Diejen model generated by gauge and integral transformations

Cites Work

• Unnamed Item
• Unnamed Item
• Source identity and kernel functions for elliptic Calogero-Sutherland type systems
• Deformed Macdonald-Ruijsenaars operators and super Macdonald polynomials
• A unified construction of generalized classical polynomials associated with operators of Calogero-Sutherland type
• Kernel functions for difference operators of Ruijsenaars type and their applications
• Zero-eigenvalue eigenfunctions for differences of elliptic relativistic Calogero-Moser hamiltonians
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Quantum completely integrable systems connected with semi-simple Lie algebras
• Calogero operator and Lie superalgebras
• Deformed quantum Calogero-Moser problems and Lie superalgebras
• Macdonald polynomials and algebraic integrability
• A multispecies Calogero-Sutherland model
• On the \(\mathcal{N}=2\) superconformal index and eigenfunctions of the elliptic RS model
• Explicit solution of the (quantum) elliptic Calogero-Sutherland model
• Singular eigenfunctions of Calogero-Sutherland type systems and how to transform them into regular ones
• Algorithms to solve the (quantum) Sutherland model
• Source identity and kernel functions for Inozemtsev-type systems
• Kernel functions and Bäcklund transformations for relativistic Calogero-Moser and Toda systems
• Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model
• A Recursive Construction of Joint Eigenfunctions for the Hyperbolic Nonrelativistic Calogero-Moser Hamiltonians
• New integrable generalizations of Calogero–Moser quantum problem
• Integrability of difference Calogero–Moser systems
• First order analytic difference equations and integrable quantum systems
• Erratum: Solution of the one-dimensional N-body problems with quadratic and/or inversely quadratic pair potentials [J. Math. Phys. 12, 419–436 (1971)]