Generalized Macdonald-Ruijsenaars systems

  title={Generalized Macdonald-Ruijsenaars systems},
  author={Misha Feigin and Alexey Silantyev},
  journal={arXiv: Quantum Algebra},
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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A bispectral q-hypergeometric basis for a class of quantum integrable models
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
Quantum Lax Pairs via Dunkl and Cherednik Operators
  • O. Chalykh
  • Mathematics, Physics
    Communications in Mathematical Physics
  • 2019
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
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It is shown that the deformed Macdonald-Ruijsenaars operators can be described as the restrictions on certain affine subvarieties of the usual Macdonald- Ruijsenaars operator in infinite number of
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