  We analyze the algebra of observables and the physical Fock space of the
finite Chern-Simons matrix model. We observe that the minimal algebra of
observables acting on that Fock space is identical to that of the Calogero
model. Our main result is the identification of the states in the l-th tower of
the Chern-Simons matrix model Fock space and the states of the Calogero model
with the interaction parameter nu=l+1. We describe quasiparticle and quasihole
states in the both models in terms of Schur functions, and discuss some
nontrivial consequences of our algebraic approach.
