- 可积系统黑板讨论班

The elliptic Calogero-Inozemtsev model and BC-type associative Yang-Baxter equation

组织者

安德烈·利亚希克 , 尼古拉·莱舍提金 , 许睿捷

演讲者

Maria Matushko

时间

2026年05月11日 15:30 至 16:30

地点

A7-201

摘要

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.