Lax Pairs and Spectral Curves for Calogero-Moser and Spin Calogero-Moser Systems

摘要

We summarize recent results on the construction of Lax pairs with spectralparameter for the twisted and untwisted elliptic Calogero-Moser systemsassociated with arbitrary simple Lie algebras, their scaling limits to Todasystems, and their role in Seiberg-Witten theory. We extend part of this workby presenting a new parametrization for the spectral curves for elliptic spinCalogero-Moser systems associated with SL(N).