Abstract
There are three subalgebra chains in Ginocchio's so(8) model. The subalgebra so(5)+su(2) and so(7) are maximum subalgebras in so(8). The subalgebra so(6) is not this case. We can find a new subalgebra so(7) between the so(8) and so(6). It is useful in the calculation at least.
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