Conformal field theory and the solution of the (quantum) elliptic Calogero-Sutherland system

Abstract

We review the construction of a conformal field theory model which describes anyons on a circle and at finite temperature, including previously unpublished results. This anyon model is closely related to the quantum elliptic Calogero-Sutherland (eCS) system. We describe this relation and how it has led to an explicit construction of the eigenvalues and eigenfunctions of the eCS system.

v2: minor corrections; references added. 18 pages, contribution to conference ``Non-commutative geometry and representation theory in mathematical physics'' in Karlstad (Sweden), 5-10 July 2004