Higher Order Deformed Elliptic Ruijsenaars Operators

@article{Hallns2022HigherOD,
  title={Higher Order Deformed Elliptic Ruijsenaars Operators},
  author={Martin A. Halln{\"a}s and Edwin Langmann and Masatoshi Noumi and Hjalmar Rosengren},
  journal={Communications in Mathematical Physics},
  year={2022}
}
We present four infinite families of mutually commuting difference operators which include the deformed elliptic Ruijsenaars operators. The trigonometric limit of this kind of operators was previously introduced by Feigin and Silantyev. They provide a quantum mechanical description of two kinds of relativistic quantum mechanical particles which can be identified with particles and anti-particles in an underlying quantum field theory. We give direct proofs of the commutativity of our operators… 
1 Citations
From Kajihara’s transformation formula to deformed Macdonald–Ruijsenaars and Noumi–Sano operators
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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