2
$\begingroup$

I know how to use young tableaus to find irreducible representations and their dimensions of $SU(n)$. Are there similar rules for $SO(n)$?

$\endgroup$
  • 2
    $\begingroup$ Yes, see e.g. arxiv.org/abs/1411.7351. In particular footnote 1 and refs. therein. $\endgroup$ – MannyC Jan 26 '19 at 21:01
  • 1
    $\begingroup$ See also doi.org/10.1063/1.1665778 $\endgroup$ – ZeroTheHero Jan 26 '19 at 21:11
  • $\begingroup$ I recommend learning about roots, weights, and the Weyl dimension formula. These work for any simple Lie algebra. I think Young tableaux work for only some. $\endgroup$ – G. Smith Jan 27 '19 at 4:04
  • $\begingroup$ You can first determine the GL irreps by projecting the tensor onto the relevant Young tableaux corresponding to the allowed partitions. Then, the SO irreps are the GL ones with the trace removed. Their dimension is given by King's rule. So in total, GL irreps=SO irreps + traces. $\endgroup$ – kospall Apr 25 at 10:12
  • $\begingroup$ Could you give some more information on King's rule? I googled it but I didn't find anything. Also I don't know much about GL irreps. I guess what you mean is the decomposition of a general tensor in symmetric, antisymmetric and trace parts? $\endgroup$ – toaster Apr 27 at 13:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.