  We assemble the spectrum of single-trace operators in free N=4 SU(N) SYM
theory into irreducible representations of the Higher Spin symmetry algebra
hs(2,2|4). Higher Spin representations or YT-pletons are associated to Young
tableaux (YT) corresponding to representations of the symmetric group
compatible with the cyclicity of color traces. After turning on interactions,
YT-pletons decompose into infinite towers of representations of the
superconformal algebra PSU(2,2|4) and anomalous dimensions are generated. We
work out the decompositions of tripletons with respect to the N=4
superconformal algebra PSU(2,2|4) and compute their one anomalous dimensions at
large N. We then focus on operators/states sitting in semishort superconformal
multiplets. By passing them through a semishort-sieve that removes
superdescendants, we derive compact expressions for the partition function of
semishort primaries.
