I am working on all of the problems from Georgi's book in Lie algebras in particle physics (independent study), but I am stuck on one of them. The question is the following:(adsbygoogle = window.adsbygoogle || []).push({});

"Find (2,1)x(2,1) (in su(3) using Young tableaux). Can you determine which representations appear antisymmetrically in the tensor product, and which appear symmetrically?"

I understand the first part, and I get that (diagram - representation - dimension)

xxx (2,1) [15]

x

times

xxx (2,1) [15]

x

=

xxxxxx (4,2) [60]

xx

+

xxxxxx (5,0) [21]

x

x

+

xxxxx (2,3) [42]

xxx

+

xxxxx (3,1) [24]

xx

x

+

xxxx (0,4) [15]

xxxx

+

xxxx (1,2) [15]

xxx

x

+

xxx (0,1) [3]

xxx

xx

+

xxxxx (3,1) [24]

xx

x

+

xxxx (1,2) [15]

xxx

x

+

xxxx (2,0) [6]

xx

xx

I don't quite get the second part. How can one determine from this which representations appear symmetrically or antisymmetrically in the tensor product? Any suggestions?

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# Young tableaux and tensor product

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