Abstract
The main results of the present paper are given in Tables 1 and 2. We have obtained all irreducible unitary representations of the conformal group and we have also found the explicit form of the invariant bilinear Hermitian form for all the representations (both unitary and nonunitary) for which it exists. Considerable interest attaches to the determination of the characters of the irreducible representations and also the decomposition of the regular representation. These questions will be considered in following publications for the general case of SO (p, q).
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