In particle physics, one often uses the dimensionality of the irrep to label the irrep (apparently this is not a very good idea since the dimension does not unambiguously determine the rep.). What are the rules one can use to simplify calculations involving direct sums. I have this one example of a direct product that on the right hand side contains many repeating terms:
For instance, suppose you have something like $D = 10\otimes 8 \oplus 10\otimes 8.$ If I have done my calculations right one should get for each term in $SU(3)$
$$\mathbf{10}\otimes \mathbf{8} = \mathbf{35}+\mathbf{27}+\mathbf{10}+\mathbf{8}$$ so that (dropping the bold notation) $$\tag{1}10\otimes 8\oplus 10\otimes 8 = 35\oplus27\oplus10\oplus8\oplus 35\oplus27\oplus10\oplus8. $$
Is there a way to simplify the right hand side of equation $(1)$ in the sense of simply writing e.g. $$\mathbf{35}\oplus\mathbf{35}\oplus\mathbf{35} = 3\cdot \mathbf{35}$$ where $3\in \mathbb{Z}.$