  We analyze SU(2) invariant half-BPS states of the 3d \cN=8 or \cN=6 SCFT
within the radial quantization of the ABJM theory, the theory proposed to
describe N M2-branes in the R^3x C^4/Z_k background. After studying the
classical moduli space of these configurations, we explicitly construct a set
of gauge invariant operators involving 't Hooft monopole operators
corresponding to these states. We show there is a one--to--one correspondence
between the two sets carrying R-charge J and that they are labeled by Young
tableaux of J boxes with a maximum of N rows. Restricting the full path
integral to this half-BPS sector of the theory, we show the latter is described
in terms of N fermions in a 2d harmonic potential in the sector of vanishing
angular momentum. The same classification, though in the N to infinity limit,
arise from the plane-wave (BMN) Matrix theory as well as the 11 dimensional LLM
bubbling geometries, providing supportive evidence for the ABJM theory and/or
the Matrix model.
