From Kajihara’s transformation formula to deformed Macdonald–Ruijsenaars and Noumi–Sano operators

@article{Hallnas2021FromKT,
  title={From Kajihara’s transformation formula to deformed Macdonald–Ruijsenaars and Noumi–Sano operators},
  author={Martin A. Hallnas and Edwin Langmann and Masatoshi Noumi and Hjalmar Rosengren},
  journal={Selecta Mathematica},
  year={2021}
}
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 formula, we deduce kernel identities for deformed Macdonald–Ruijsenaars (MR) and Noumi–Sano (NS) operators. The deformed MR operators were introduced by Sergeev and Veselov in the first order case and by Feigin and Silantyev in the higher order cases. As applications of our kernel identities, we prove that… 
2 Citations
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