Coset constructions in Chern-Simons gauge theory

Abstract Coset constructions in the framework of Chern-Simons topological gauge theories are studied. Two examples are considered: models of the types [ U (1) p × U (1) q ] U (1) p+q ≌ U (1) pq(p+q) with p and q coprime integers, and [ SU (2) m × SU (2) 1 ] SU (2) m+1 . In the latter case it is shown that the Chern-Simons wave-functionals can be identified with the characters of the minimal unitary models, and an explicit representation of the knot (Verlinde) operators acting on the space of c