  Character formulae for positive energy unitary representations of the N=4
superconformal group are obtained through use of reduced Verma modules and Weyl
group symmetry. Expansions of these are given which determine the particular
representations present and results such as dimensions of superconformal
multiplets. By restriction of variables various `blind' characters are also
obtained. Limits, corresponding to reduction to particular subgroups, in the
characters isolate contributions from particular subsets of multiplets and in
many cases simplify the results considerably. As a special case, the index
counting short and semi-short multiplets which do not form long multiplets
found recently is shown to be related to particular cases of reduced
characters. Partition functions of N=4 super Yang Mills are investigated.
Through analysis of these, exact formulae are obtained for counting half and
some quarter BPS operators in the free case. Similarly, partial results for the
counting of semi-short operators are given. It is also shown in particular
examples how certain short operators which one might combine to form long
multiplets due to group theoretic considerations may be protected dynamically.
