Abstract
The Clebsch–Gordan coefficients for the product (1001)⊗(1001), where (1001) is the adjoint representation of SU(5), with respect to the group basis and the subgroup basis in the reduction SU(5)⊇SU(3)×SU(2)×U(1) are computed. One of the basic tools in this computation is the exhaustive use of the Verma algorithm to find bases for the weight subspaces of dimension higher than 1. It allows for the construction of bases in a systematic way by using the so-called Verma inequalities. Only the coefficients for the dominant weights are calculated. The other ones can be obtained by using the elements of finite order (charge conjugation operators) of SU(5).
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