Loop groups, anyons and the Calogero-Sutherland model

The positive energy representations of the loop group of U(1) are used to c onstruct a boson-anyon correspondence. We compute all the correlation funct ions of our anyon fields and study an anyonic W-algebra of unbounded operat ors with a common dense domain. This algebra contains an operator with pecu liar exchange relations with the anyon fields. This operator can be interpr eted as a second quantized Calogero-Sutherland (CS) Hamiltonian and may be used to solve the CS model. In particular, we inductively construct all eig enfunctions of the CS model from anyon correlation functions, for all parti cle numbers and positive couplings.