Duality and Macdonald difference operators

2023/03/07 by Di Francesco, Philippe, Kedem, Rinat
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2303.04276

Abstract

This note summarizes certain properties common to Macdonald, Koornwinder and Arthamonov-Shakirov q-difference operators, relating to the duality or bi-spectrality properties of their eigenfunctions. This results in Pieri operators which, in the q-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.

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