BIMSA > Integrable systems blackboard seminar Integrable systems blackboard seminar The elliptic Calogero-Inozemtsev model and BC-type associative Yang-Baxter equation
The elliptic Calogero-Inozemtsev model and BC-type associative Yang-Baxter equation
Organizers
Andrii Liashyk , Nicolai Reshetikhin , Ruijie Xu
Speaker
Maria Matushko
Time
Monday, May 11, 2026 3:30 PM - 4:30 PM
Venue
A7-201
Abstract
The Calogero-Inozemtsev model is an elliptic integrable many-body system with five coupling constants, generalizing the $BC_n$-type Calogero model. In this talk, I will explain how to construct a matrix generalization of this model from the elliptic Baxter-Belavin quantum R-matrix and the corresponding elliptic boundary $K$-matrix depending on five parameters. The main tool for proving integrability is that $R$ and $K$ satisfy not only the reflection equation, but also a quadratic relation known as the $B$C-type associative Yang-Baxter equation. I will also discuss the link to boundary Knizhnik-Zamolodchikov equations: in the quasi-classical limit, a solution of the $BC$-type associative Yang-Baxter equation yields the corresponding flat $KZ$ connection.