Singletons on AdSn

2000

We define the singletons for the invariance group \( {\overline S _n} = {\overline {SO} _0}\left( {2,n - 1} \right) \)) of the AdS n space-time. We write down some of their important properties and characterizations. It is found that the tensor product of singletons of spin 0 or 1/2 decomposes into representations that are a kind of massless representations of S n . Other kinds of massless representations, related to singletons, are also studied and a comparison is made. Various Gupta-Bleuler triplets are constructed for singletons and for massless representations.