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We study the minimal unitary representation (minrep) of SO(5,2), obtained byquantization of its geometric quasiconformal action, its deformations andsupersymmetric extensions. The minrep of SO(5,2) describes a massless conformalscalar field in five dimensions and admits a unique "deformation" whichdescribes a massless conformal spinor. Scalar and spinor minreps of SO(5,2) arethe 5d analogs of Dirac's singletons of SO(3,2). We then construct the minimalunitary representation of the unique 5d superconformal algebra F(4) with theeven subalgebra SO(5,2) X SU(2). The minrep of F(4) describes a masslessconformal supermultiplet consisting of two scalar and one spinor fields. Wethen 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) vanishesidentically as operators and hence its enveloping algebra yields theAdS_6/CFT_5 bosonic higher spin algebra directly. The enveloping algebra of thespinor minrep defines a "deformed" higher spin algebra for which a deformedJoseph ideal vanishes identically as operators. These results are then extendedto the construction of the unique higher spin AdS_6/CFT_5 superalgebra as theenveloping algebra of the minimal unitary realization of F(4) obtained by thequasiconformal methods.

Minimal unitary representation of 5d superconformal algebra F(4) and AdS_6/CFT_5 higher spin (super)-algebras