I know how to calculate the CG coefficients for $SU(N)$, but there are other simple Lie group like $SO(N)$ and $Sp(N)$. But up to now I can't find any textbook tells me how to calculate these and I also can't find tables for these. So where I can find tables of CG coefficients for $SO(N)$ and $Sp(N)$. Really thanks.
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1$\begingroup$ Part of your problem is probably that mathematicians generally do not call them Clebsch-Gordan coefficients. Usually one would just talk about the decomposition of tensor products of representations of SO(n)/Sp(n) into irreducible representations, or in the type A case you'd call them Littlewood-Richardson coefficients. There are several different softwares that can compute this for you, e.g. LiE or SAGE. $\endgroup$– Dan PetersenCommented May 5, 2017 at 4:55
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$\begingroup$ @Dan: I think the OP is asking about something else which is what physicists call Clebsch-Gordan coefficients. These are matrix elements of intertwiners or elements of ${\rm Hom}_G(U\otimes V, W)$ where $U,V,W$ are irreducible representations. Although "I know how to calculate CG coefficients for $SU(N)$" sounds goofy to me. Rather little is know about them for $N>2$. $\endgroup$– Abdelmalek AbdesselamCommented May 5, 2017 at 14:23
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$\begingroup$ @AbdelmalekAbdesselam homepages.physik.uni-muenchen.de/~vondelft/Papers/ClebschGordan There is website for computing these coefficients. Certainly I can't calculate specific number unless N is 2 or 3, and I just know where I can find the general algorithm and if the N is not large enough, this website can tell me the answer. It may be enough for practical use in physics. $\endgroup$– fff123123Commented May 5, 2017 at 16:34
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