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The group SU2(C) has this property. What other groups share it?

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3 
 Is this a real question? – Bruce Westbury Nov 29 2011 at 13:41
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 an irreducible representation? – mcampo Nov 29 2011 at 13:55
What exactly is the question? Do you want an example (easy)? A complete classification (impossible)? – Igor Rivin Nov 29 2011 at 13:59
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 A direct product of SU2 with any group you like. – Noah Snyder Nov 29 2011 at 15:29
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 Incidentally, if you want there to be exactly one irrep of dimension n for all n, then the tensor category of representations has to be Rep(SU(2)). But that leaves open weird options like SU(2)xG where G has no nontrivial finite dimensional representations. – Noah Snyder Nov 29 2011 at 16:05

closed as not a real question by Bruce Westbury, Mark Sapir, Igor Rivin, Andreas Blass, Noah Snyder Nov 29 2011 at 16:05

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