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Symmetric polynomials: DIM integrable systems versus twisted Cherednik systems

High Energy Physics - Theory 2026-04-30 v2 Mathematical Physics Combinatorics math.MP Quantum Algebra

Abstract

We discuss interrelations between eigenfunctions of the Hamiltonians associated with the commutative (integer ray) subalgebras of the Ding-Iohara-Miki algebra and those of the twisted Cherednik system. In the case of t=qmt=q^{-m} with natural mm, eigenfunctions of the first system of Hamiltonians are the twisted Baker-Akhiezer functions (BAFs) introduced by O. Chalykh, while eigenfunctions of the twisted Cherednik Hamiltonians are twisted non-symmetric Macdonald polynomials. Actually, the twisted Cherednik ground state is symmetric and coincides with a peculiar symmetric BAF. We lift this correspondence to excited states, and claim that both Cherednik eigenfunctions and BAF's can be combined to produce symmetric functions, which coincide with each other and are eigenfunctions of the both DIM Hamiltonians and power sums of the twisted Cherednik Hamiltonians at once. This reflects the correspondence between the DIM algebra and the spherical DAHA explicitly.

Cite

@article{arxiv.2601.19878,
  title  = {Symmetric polynomials: DIM integrable systems versus twisted Cherednik systems},
  author = {A. Mironov and A. Morozov and A. Popolitov},
  journal= {arXiv preprint arXiv:2601.19878},
  year   = {2026}
}

Comments

12 pages, LaTeX

R2 v1 2026-07-01T09:22:42.324Z