  The positive energy representations of the loop group of U(1) are used to
construct a boson-anyon correspondence. We compute all the correlation
functions of our anyon fields and study an anyonic W-algebra of unbounded
operators with a common dense domain. This algebra contains an operator with
peculiar exchange relations with the anyon fields. This operator can be
interpreted as a second quantised Calogero-Sutherland (CS) Hamiltonian and may
be used to solve the CS model. In particular, we inductively construct all
eigenfunctions of the CS model from anyon correlation functions, for all
particle numbers and positive couplings.
