Duality in elliptic Ruijsenaars system and elliptic symmetric functions

@inproceedings{Mironov2021DualityIE,
  title={Duality in elliptic Ruijsenaars system and elliptic symmetric functions},
  author={Andrei Mironov and A. Morozov and Yegor Zenkevich},
  year={2021}
}
We demonstrate that the symmetric elliptic polynomials Eλ(x) originally discovered in the study of generalized Noumi-Shiraishi functions are eigenfunctions of the elliptic Ruijsenaars-Schneider (eRS) Hamiltonians that act on the mother function variable yi (substitute of the Young-diagram variable λ). This means they are eigenfunctions of the dual eRS system. At the same time, their orthogonal complements in the Schur scalar product, PR(x) are eigenfunctions of the elliptic reduction of the… 
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