The associative Yang-Baxter equation and R-matrix Lax pairs for Calogero models

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.

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.