Description
We describe a general family of non-Abelian FQHE states at \nu = k/(km + r)
with polynomial wavefunctions \prod_{i<j}(z_i- z_j)^m J_\lambda^\alpha
(z1;...; zN) where J_\lambda^\alpha is a symmetric Jack polynomial with
negative (coprime) rational parameter \alpha =-(k+1)/(r-1), and \lambda is a
compressed partition. These polynomials are dominated by an occupation-
number pattern maximally-obeying the generalized Pauili rule that no
(consecutive) group of (km + r) orbitals contains more than k particles and
(m>0) no group of m orbitals contains more than one. This exclusion rule
defines a space of polynomials characterized by how they vanish as clusters of
particle coordinates contract to a point. The edge of these FQHE states has a
fractionally-quantized thermal Hall effect with c^{eff} = k(r + 1)/(k + r),
derived from the exclusion rule. The r = 2 family are the Laughlin, Moore-Read,
and Read-Rezayi states, related to unitary conformal field theories. The r > 2
families are related to non-unitary W^{k+1;k+r}_k cft, but (as polynomials)
have well-defined (not obtainable from CFT) quasi-hole propagators, which
overcomes the principal objection to the proposition that non-unitary cft's can
describe FQHE states. The m = 1, r = k + 1 set are a non-Abelian alternative
construction of states at 2/5,3/7,4/9, . . . .. We also present model
wavefunctions for quasiparticle (as opposed to quasihole) excitations of the
$Z_k$ parafermion sequence (Laughlin/Moore-Read/Read-Rezayi) of Fractional
Quantum Hall states. These states satisfy two generalized clustering conditions:
they vanish when either a cluster of $k+2$ electrons is put together, or when
two clusters of $k+1$ electrons are formed at different positions. For Abelian
Fractional Quantum Hall states ($k=1$), our construction reproduces the Jain
quasielectron wavefunction, and elucidates the difference between the Jain and
Laughlin quasiparticle constructions. For two (or more) quasiparticles, our states
differ from those constructed using Jain's method. By adding our quasiparticles
to the Laughlin state, we obtain a hierarchy scheme which gives rise to a non
abelian Jack $\nu=\frac{2}{5}$ FQH state (same as the Gaffnian) with great
overlap with the Jain states.
