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BIMSA Integrable Systems Seminar
The associative Yang-Baxter equation and R-matrix Lax pairs for Calogero models
The associative Yang-Baxter equation and R-matrix Lax pairs for Calogero models
Organizers
Speaker
Maria Matushko
Time
Monday, March 31, 2025 5:00 PM - 6:00 PM
Venue
A3-1a-205
Online
Zoom 873 9209 0711
(BIMSA)
Abstract
The elliptic Calogero-Moser system 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 $B$-type associative Yang-Baxter equations to the similar relations depending on the spectral parameters and to construct an $R$-matrix valued Lax pair in terms of the $8$-vertex elliptic R-matrix for the Calogero-Inozemtsev system.
I will tell how to extend the Kirillov's $B$-type associative Yang-Baxter equations to the similar relations depending on the spectral parameters and to construct an $R$-matrix valued Lax pair in terms of the $8$-vertex elliptic R-matrix for the Calogero-Inozemtsev system.