For the quantum Calogero-Moser model, we construct a set of conserved
operators and another set of operators, named boost operators, from it
s Lax operator. We prove that each conserved operator satisfies both t
he Lax equation and a remarkable relation named additional relation. F
rom these knowledge, we show that the conserved operators are involuti
ve. Moreover, the conserved operators and the boost operators constitu
te the U(1)-current algebra. All the proofs are simplified a great dea
l due to the Lax equations and additional relations.