Is SU(2) the key to understanding quantum numbers and symmetry?

TrickyDicky
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Is it purely coincidental that the internal symmetry related flavor quantum numbers(like isospin and weak isospin) and the spacetime symmetry related spin quantum number have SU(2) as underlying group?
They refer to seemingly unrelated things but it is remarkable how ubiquitous SU(2) is.
 
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Yes, mere coincidence. In the absence of supersymmetry.
 
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