CHIRAL OPERATOR PRODUCT ALGEBRA HIDDEN IN CERTAIN FRACTIONAL QUANTUM HALL WAVE-FUNCTIONS

In this paper we study the conditions under which an N-electron wave f unction for a fractional quantum Hall (FQH) state can be viewed as an N-point correlation function in a conformal field theory (CFT). Severa l concrete examples are presented to illustrate, when these conditions are satisfied, how to ''derive'' or ''uncover'' a relevant operator a lgebra in the associated CFT from the FQH wave functions. Besides the known pfaffian state, the states studied here include three d-wave pai red states, one for spinless electrons and two for spin-1/2 electrons (one of them is the Haldane-Rezayi state). It is suggested that the no n-abelian topological order hidden in these states can be characterize d by their associated chiral operator product algebra, from which one may infer the quantum numbers of quasiparticles and calculate their wa ve functions.