Minimal unitary representation of 5d superconformal algebra F(4) and AdS₆/CFT₅ higher spin (super)-algebras

We study the minimal unitary representation (minrep) of SO(5,2), obtained by quantization of its geometric quasiconformal action, its deformations and supersymmetric extensions. The minrep of SO(5,2) describes a massless conformal scalar field in five dimensions and admits a unique "deformation" which describes a massless conformal spinor. Scalar and spinor minreps of SO(5,2) are the 5. d analogs of Dirac's singletons of SO(3,2). We then construct the minimal unitary representation of the unique 5. d superconformal algebra F(4) with the even subalgebra SO(5,2)×SU(2). The minrep of F(4) describes a massless conformal supermultiplet consisting of two scalar and one spinor fields. We then extend our results to the construction of higher spin AdS₆/CFT₅ (super)-algebras. The Joseph ideal of the minrep of SO(5,2) vanishes identically as operators and hence its enveloping algebra yields the AdS₆/CFT₅ bosonic higher spin algebra directly. The enveloping algebra of the spinor minrep defines a "deformed" higher spin algebra for which a deformed Joseph ideal vanishes identically as operators. These results are then extended to the construction of the unique higher spin AdS₆/CFT₅ superalgebra as the enveloping algebra of the minimal unitary realization of F(4) obtained by the quasiconformal methods.