2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98352A 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.Minor corrections: report number is changedHigh Energy Physics - Theorytext