Speaker
Description
The rational Calogero-Sutherland-Moser model is originally a system of identical particles scattering on the line with inverse-square potential. There are also trigonometric, hyperbolic and elliptic version of this model. The integrability of the model follows from the presence of a Lax pair.
The Calogero system of type $A$ admits the so-called $R$-matrix Lax pair presentation, the matrix elements are expressed in terms of the quantum $GL_N$ Baxter-Belavin elliptic $R$-matrices. For $N = 1$ this construction reproduces the Krichever’s Lax pair with spectral parameter. The equations of motion follow from the associative Yang-Baxter equation for the elliptic Baxter-Belavin R-matrix.
I will tell how to extend the Kirillov's ${\rm B}$-type associative Yang-Baxter equations to the similar relations depending on the spectral parameters and to construct an $R$-matrix valued for the Calogero-Inozemtsev of ${\rm BC}_n$ type. General construction uses the elliptic Shibukawa-Ueno $R$-operator and the Komori-Hikami $K$-operators satisfying reflection equation. Then, using the Felder-Pasquier construction the answer for the Lax pair is also written in terms of the elliptic Baxter-Belavin $R$-matrix.
The talk is based on the joint work with Andrei Zotov and Artem Mostovskii arXiv:2503.22659
