Let's consider about the Baryon octet diagram. We can identify the isospin $I_3$ symmetry by noticing the mirror symmetry with respect to the $I_3$, i.e. x-axis. However, how can we expand this into $SU(3)$ flavor symmetry? How is this represented in the octet diagram?
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As a note, is it related to the representation of the generators of $SU(3)$? Or, if that is not the case, is it related to the root system of $SU(3)$? – Nugi Nov 25 '19 at 01:16
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Yes. See here and here and here. Can you sharpen your question using this standard language? – Cosmas Zachos Nov 25 '19 at 02:40
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Related : Symmetry in terms of matrices. – Frobenius Nov 25 '19 at 03:54