Clebsch-Gordan coefficients for \(E_ 6\) and SO(10) unification models. (English) Zbl 0556.22011
A method for computing Clebsch-Gordan coefficients (CGC) for \(E_ 6\) and SO(10)\(\subset E_ 6\) is given. One considers the tensor product, 27\(\otimes 27\), of the irreducible representation (100 000) of \(E_ 6\) with itself. The basis vectors of the representation space are identified with the light fermions of the theory and the related CGC are calculated. The main idea is to calculate only some representative CGC and then to give a prescription how any other CGC can be readily identified with one of the representatives. The identification is made by using the operators which permute the basis vectors in the representation space. The CGC are calculated thrice: once in a basis independent of any semisimple subgroup, then in a basis which refers to \(SO(10)\subset E_ 6\), and finally in a basis referring to \(SU(5)\subset SO(10)\subset E_ 6\). An example of CGC of 27\(\otimes 27\) relative to the \(SU(3)\times SU(2)\times U(1)\subset SU(5)\subset SO(10)\subset E_ 6\) basis is given.
Reviewer: G.Zet
MSC:
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
References:
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