Can anyone explain to me why(adsbygoogle = window.adsbygoogle || []).push({});

the 3-rep of SU(3) gives

[itex]3\otimes 3 = \overline{3}\oplus 6[/itex]

whereas for the 5 of SU(5)

[itex]5\otimes 5 = 10\oplus 15[/itex]?

I thought the general pattern was

[itex]N \otimes N = \overline{\frac{1}{2}N(N-1)}\oplus \frac{1}{2}N(N+1)[/itex]

but this second example seems to contradict that.

Edit: I wrote 15* instead of 15.

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# Decomposition of direct product into symmetric/antisymmetric parts

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