  I review the relationship between AdS/CFT (anti-de Sitter / conformal field
theory) dualities and the general theory of positive energy unitary
representations of non-compact space-time groups and supergroups. I show, in
particular, how one can go from the manifestly unitary compact basis of the
lowest weight (positive energy) representations of the conformal group (Wigner
picture) to the manifestly covariant coherent state basis (Dirac picture). The
coherent states labelled by the space-time coordinates correspond to covariant
fields with a definite conformal dimension. These results extend to higher
dimensional Minkowskian spacetimes as well as generalized spacetimes defined by
Jordan algebras and Jordan triple systems. The second part of my talk discusses
the extension of the above results to conformal supergroups of Minkowskian
superspaces as well as of generalized superspaces defined by Jordan
superalgebras. The (super)-oscillator construction of generalized
(super)-conformal groups can be given a dynamical realization in terms of
generalized (super)-twistor fields.
