Duality and Macdonald difference operators
arXiv:2303.04276
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.
14 pages