Elliptic Calogero-Moser Systems and Isomonodromic Deformations

“A`−1” stands for the A`−1 root system that underlies this model. Similarly, an elliptic Calogero-Moser system can be defined for each irreducible (but not necessary reduced) root system. Furthermore, for non-simply laced root systems, a kind of variants called “twisted model” and “extended twisted models” are also known. Those elliptic Calogero-Moser systems are known to possess an isospectral Lax pair L(z) and M(z). z is an “elliptic spectral parameter”, i.e., a parameter that lives on the torus Eτ = C/(Z+ τZ). The equations of motion can be written in the Lax form