  A simple realization of the conformal higher spin symmetry on the free $3d$
massless matter fields is given in terms of an auxiliary Fock module both in
the flat and $AdS_3$ case. The duality between non-unitary field-theoretical
representations of the conformal algebra and the unitary (singleton--type)
representations of the $3d$ conformal algebra $sp(4,\R)$ is formulated
explicitly in terms of a certain Bogolyubov transform.
