Abstract
For the exceptional Lie algebra E6 minimal SO(3) tensor operator realizations are constructed which correspond to the maximal decomposition of E6 in the respective chains E6⊃F4⊃SO(3), E6⊃SU(3)⊗G2⊃SO(3)⊗SO(3), E6⊃F4⊃SO(3)⊗G2⊃SO(3)⊗SO(3), E6⊃Sp(8)⊃SO(3), and E6⊃G2⊃SO(3). Two particular realizations are shown to provide a basis in which certain structural zeros of Racah’s 6j-symbol can be explained.
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