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Duality and Macdonald difference operators

Mathematical Physics 2023-03-09 v1 Combinatorics math.MP Representation Theory

Abstract

This note summarizes certain properties common to Macdonald, Koornwinder and Arthamonov-Shakirov qq-difference operators, relating to the duality or bi-spectrality properties of their eigenfunctions. This results in Pieri operators which, in the qq-Whittaker limit, are relativistic difference Toda type Hamiltonians which have a related quantum cluster algebra structure known as the quantum Q-system. The genus-2 result explained here is new.

Keywords

Cite

@article{arxiv.2303.04276,
  title  = {Duality and Macdonald difference operators},
  author = {Philippe Di Francesco and Rinat Kedem},
  journal= {arXiv preprint arXiv:2303.04276},
  year   = {2023}
}

Comments

14 pages

R2 v1 2026-06-28T09:06:35.434Z