  We exhibit the elliptic Calogero-Moser system as a Hitchin system of
G-principal Higgs pairs. The group G, though naturally associated to any root
system, is not semi-simple. We then interpret the Lax pairs with spectral
parameter of [dP1] and [BSC1] in terms of equivariant embeddings of the Hitchin
system of G into that of GL(N).
