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 AdS 6 / CFT 5 (super)-algebras. The Joseph ideal of the minrep of SO ( 5 , 2 ) vanishes identically as operators and hence its enveloping algebra yields the AdS 6 / CFT 5 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 AdS 6 / CFT 5 superalgebra as the enveloping algebra of the minimal unitary realization of F ( 4 ) obtained by the quasiconformal methods.
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