Quasiconformal Group Approach to Higher Spin Algebras, Their Deformations and Supersymmetric Extensions

The quasiconformal method provides us with a unified approach to the construction of minimal unitary representations (minrep) of noncompact groups, their deformations as well as their supersymmetric extensions. We review the quasiconformal construction of the minrep of SO(d, 2), its deformations and their applications to unitary realizations of AdS((d+1))/CFTd higher spin algebras and their deformations for arbitrary d and supersymmetric extensions for d <= 6. AdS((d+1))/CFTd higher spin algebras, their deformations and supersymmetrie extensions are given by the enveloping algebras of the quasiconformal realizations of the minrep, its deformations and supersymmetric extensions, respectively, and are in one-to-one correspondence with massless conformal fields for arbitrary d and massless conformal supermultiplets for d <= 6.