For discrete groups, we can easily find the decomposition of the direct product of irreducible representations with the help of the character table. All we need to do is multiply the characters of the irreducible representations to get the characters of the direct product representation and then use the orthogonality relations to find the multiplicity of each of the irreps in the direct product representation.(adsbygoogle = window.adsbygoogle || []).push({});

Is there an easy way to do something similar for Lie groups? Let two representations of a Lie group be given in terms of their highest weights. I am wondering if there is a straightforward and easy technique to find the decomposition of the direct product of those representations into a direct sum of irreducible representations.

For example for SU(3) group how can we calculate

3x8=15+6bar+3

or in terms of the highest weights

(1,0)x(1,1)=(2,1)+(0,2)+(1,0) ?

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# Director product expansion of Lie groups.

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