Generalized Macdonald-Ruijsenaars systems

@article{Feigin2011GeneralizedMS,
  title={Generalized Macdonald-Ruijsenaars systems},
  author={Misha Feigin and Alexey Silantyev},
  journal={arXiv: Quantum Algebra},
  year={2011}
}
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9 Citations
Background Citations
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9 Citations

Super-Macdonald Polynomials: Orthogonality and Hilbert Space Interpretation
The super-Macdonald polynomials, introduced by Sergeev and Veselov, generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and they are eigenfunctions of the deformed…
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Kajihara obtained in 2004 a remarkable transformation formula connecting multiple basic hypergeometric series associated with A-type root systems of different ranks. By specialisations of his…
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We establish orthogonality relations for the Baker–Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik–Macdonald–Mehta integral for these…
Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions
Higher Order Deformed Elliptic Ruijsenaars Operators
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Quantum Lax Pairs via Dunkl and Cherednik Operators
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We establish a direct link between Dunkl operators and quantum Lax matrices $${{\mathcal{L}}}$$L for the Calogero–Moser systems associated to an arbitrary Weyl group W (or an arbitrary finite…
Source Identities and Kernel Functions for the Deformed Koornwinder–van Diejen Models
We consider generalizations of the BC -type relativistic Calogero–Moser–Sutherland models, comprising of the rational, trigonometric, hyperbolic, and elliptic cases, due to Koornwinder and van…
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We present how explicit eigenfunctions of the principal Hamiltonian for the BCm relativistic Calogero-Moser-Sutherland model, due to van Diejen, can be constructed using gauge and integral…
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For the class of quantum integrable models generated from the $q-$Onsager algebra, a basis of bispectral multivariable $q-$orthogonal polynomials is exhibited. In a first part, it is shown that the…

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