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 -difference operators, relating to the duality or bi-spectrality properties of their eigenfunctions. This results in Pieri operators which, in the -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.
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}
}
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14 pages