On the representations of the group SU(3)

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Abstract
By a generalization of techniques developed earlier for dealing with the three-dimensional rotation group O3 the generators of the group SU(3) are expressed as differential operators involving four independent variables. The reduction in the number of variables simplifies the mathematical problem and makes it easier to study the properties of the group and its irreducible representations. From the forms of the new operators it becomes apparent that the basic states of an irreducible representation of SU(3) are linear combinations of Clebsch-Gordan series of SU(2) (or O3). A convenient expression for the latter, which simplifies the derivation and also brings out the significance of certain steps more clearly, is obtained here by a proper interpretation of the results given in an earlier paper by the author. Besides this certain recursion relations for the Clebsch-Gordan coefficients of SU(2) are also found to be helpful for studying the SU(3) representations. These relations are derived in a novel way from Gauss's relations between contiguous hypergeometric functions.

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