- #1
joex444
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This isn't an assigned problem, just a popular forum I was hoping someone here would be able to help or move it to where it should be...
I was working out the Young's tableaux for two SU(3) representations where
[tex]3 \otimes 3 = 6 \oplus \bar{3}[/tex], where the 6 is symmetric and the 3 bar is anti-symmetric.
Now, we can also do [tex]\bar{3} \otimes \bar{3} = \bar{6} \oplus 3[/tex] but the diagrams are not pure row or columns. Here the 6 bar representation is
X X
X X
and the 3 is
X X
X
X
So, in the case of [tex]3 \otimes 3[/tex] we have (if you refer to Sakurai p.~370 where he gives the definition of p,q) the 6 representation as (p,q) = (2,0) and the 3 bar as (0,1). In the case of [tex]\bar{3} \otimes \bar{3}[/tex] we obtain a (0,2) and (1,0), as expected (?).
Anyways, would the (0,2) representation have the same symmetry as the (2,0) rep?
Homework Statement
I was working out the Young's tableaux for two SU(3) representations where
[tex]3 \otimes 3 = 6 \oplus \bar{3}[/tex], where the 6 is symmetric and the 3 bar is anti-symmetric.
Homework Equations
The Attempt at a Solution
Now, we can also do [tex]\bar{3} \otimes \bar{3} = \bar{6} \oplus 3[/tex] but the diagrams are not pure row or columns. Here the 6 bar representation is
X X
X X
and the 3 is
X X
X
X
So, in the case of [tex]3 \otimes 3[/tex] we have (if you refer to Sakurai p.~370 where he gives the definition of p,q) the 6 representation as (p,q) = (2,0) and the 3 bar as (0,1). In the case of [tex]\bar{3} \otimes \bar{3}[/tex] we obtain a (0,2) and (1,0), as expected (?).
Anyways, would the (0,2) representation have the same symmetry as the (2,0) rep?