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The discrete most degenerate principal series of irreducible Hermitian representations of the Lie algebra of an arbitrary noncompact as well as compact rotation group SO(p, q) are derived. The properties of these representations are discussed and the explicit form of the corresponding harmonic functions is given.

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Recursion and symmetry relations are obtained for the Clebsch-Gordan coefficients associated with the coupling of two SL(2, C) principal-series representations. An explicit procedure based on the recursion relations which are not restricted to the case of principal-series representations is given for generating a set of coefficients from a single "initial" coefficient. A program for the study of a possible connection, through analytic continuation, between the coupling coefficients for finite-dimensional representations and those for the infinite-dimensional case is presented.