  We obtain an exact matrix-product-state (MPS) representation of a large
series of fractional quantum Hall (FQH) states in various geometries of genus
0. The states in question include all paired k=2 Jack polynomials, such as the
Moore-Read and Gaffnian states, as well as the Read-Rezayi k=3 state. We also
outline the procedures through which the MPS of other model FQH states can be
obtained, provided their wavefunction can be written as a correlator in a 1+1
conformal field theory (CFT). The auxiliary Hilbert space of the MPS, which
gives the counting of the entanglement spectrum, is then simply the Hilbert
space of the underlying CFT. This formalism enlightens the link between
entanglement spectrum and edge modes. Properties of model wavefunctions such as
the thin-torus root partitions and squeezing are recast in the MPS form, and
numerical benchmarks for the accuracy of the new MPS prescription in various
geometries are provided.
