  It was recently discovered that fractional quantum Hall (FQH) states can be
classified by the way ground state wave functions go to zero when electrons are
brought close together. Quasiparticles in the FQH states can be classified in a
similar way, by the pattern of zeros that result when electrons are brought
close to the quasiparticles. In this paper we combine the pattern-of-zero
approach and the conformal-field-theory (CFT) approach to calculate the
topological properties of quasiparticles. We discuss how the quasiparticles in
FQH states naturally form representations of a magnetic translation algebra,
with members of a representation differing from each other by Abelian
quasiparticles. We find that this structure dramatically simplifies topological
properties of the quasiparticles, such as their fusion rules, charges, and
scaling dimensions, and has consequences for the ground state degeneracy of FQH
states on higher genus surfaces. We find constraints on the pattern of zeros of
quasiparticles that can fuse together, which allow us to obtain the fusion
rules of quasiparticles from their pattern of zeros, at least in the case of
the (generalized and composite) parafermion states. We also calculate from CFT
the number of quasiparticle types in the generalized and composite parafermion
states, which confirm the result obtained previously through a completely
different approach.
