Infinite Algebras and Intertwining Networks for Calogero Models

Explore the intricacies of Calogero models in this 50-minute lecture delivered at the Workshop on "Exactly Solvable Models" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the rational A-type case, examining the infinite algebra of symmetric observables and its inclusion of all conserved charges. Investigate the functional dependency leading to a finite but nonlinear W algebra, and learn about the construction of its first Casimir operator. Discover the concept of horizontal intertwiners and their role in relating energy spectra for integral shifts of the Calogero coupling. Gain insights into the recent discovery of vertical intertwiners, which increase the number of interacting Calogero particles by one for any fixed integer coupling. Enhance your understanding of these superintegrable quantum multi-particle models and their mathematical properties.