Abstract
All inequivalent continuous unitary irreducible representations ofS U(N, 1) (N≧2) have been determined and classified. The matrix elements of the infinitesimal generators realized on a certain Hilbert space have been derived. Representations of the groups\(\overline {SU(N,1)} \),S U(N, 1)/ZN+1,\(\overline {U(N,1)} \) andU(N, 1) are classified in a similar manner.
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