Calogero-Moser systems and Hitchin systems

We exhibit the elliptic Calogero-Moser system as a Hitchin system of G-prin cipal Higgs pairs. The group G, though naturally associated to any root sys tem, is not semi-simple. We then interpret the Lax pairs with spectral para meter of d'Hoker and Phong [dP1] and Bordner, Corrigan and Sasaki [BCS1] in terms of equivariant embeddings of the Hitchin system of G into that of G L (N).