  Possible short and semi-short positive energy, unitary representations of the
Osp(2N|4) superconformal group in three dimensions are discussed. Corresponding
character formulae are obtained, consistent with character formulae for the
SO(3,2) conformal group, revealing long multiplet decomposition at unitarity
bounds in a simple way. Limits, corresponding to reduction to various Osp(2N|4)
subalgebras, are taken in the characters that isolate contributions from fewer
states, at a given unitarity threshold, leading to considerably simpler
formulae. Via these limits, applied to partition functions, closed formulae for
the generating functions for numbers of BPS operators in the free field limit
of superconformal U(n)\times U(n) \N=6 Chern Simons theory and its supergravity
dual are obtained in the large n limit. Partial counting of semi-short
operators is performed and consistency between operator counting for the free
field and supergravity limits with long multiplet decomposition rules is
explicitly demonstrated. Partition functions counting certain protected scalar
primary semi-short operators, and their superconformal descendants, are
proposed and computed for large n. Certain chiral ring partition functions are
discussed from a combinatorial perspective.
