Group Analysis of Differential Equations and Integrable Systems − 2018

Oleg Chalykh (University of Leeds, UK)

Quantum Lax pairs for the elliptic Calogero-Moser and Ruijsenaars systems

We will present a quantum analogue of the celebrated Krichever's Lax pair with spectral parameter for the elliptic Calogero-Moser system and explain how it can be obtained from the elliptic Dunkl operators. The method works for all root systems, including $BC_n$-case with 5 coupling parameters (Inozemtsev system). We will also discuss how it extends to the elliptic Ruijsenaars system and its generalisations, where very little was known beyond $A_n$-case.

Based on arXiv:1804.01766 [math.QA].