  We extend our earlier work on the minimal unitary representation of $SO(d,2)$
and its deformations for $d=4,5$ and $6$ to arbitrary dimensions $d$. We show
that there is a one-to-one correspondence between the minrep of $SO(d,2)$ and
its deformations and massless conformal fields in Minkowskian spacetimes in $d$
dimensions. The minrep describes a massless conformal scalar field, and its
deformations describe massless conformal fields of higher spin. The generators
of Joseph ideal vanish identically as operators for the quasiconformal
realization of the minrep, and its enveloping algebra yields directly the
standard bosonic $AdS_{(d+1)}/CFT_d$ higher spin algebra. For deformed minreps
the generators of certain deformations of Joseph ideal vanish as operators and
their enveloping algebras lead to deformations of the standard bosonic higher
spin algebra. In odd dimensions there is a unique deformation of the higher
spin algebra corresponding to the spinor singleton. In even dimensions one
finds infinitely many deformations of the higher spin algebra labelled by the
eigenvalues of Casimir operator of the little group $SO(d-2)$ for massless
representations.
