 #1
ChrisVer
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Main Question or Discussion Point
I am trying to work out with Young graphs the tensor product of:
[itex] \bar{3} \otimes \bar{3} [/itex]
The problem is that I end up with:
[itex] \bar{3} \otimes \bar{3} = 15 \oplus 6 \oplus 3 \oplus 3 [/itex]
Is that correct? It doesn't seem correct at all (dimensionally speaking I should have taken something like [itex]\bar{6} \oplus 3[/itex]  like baring the [itex]3 \otimes 3 =6 \oplus \bar{3}[/itex])...
In fact I am unable to understand the rule that says:
looking from the righttoleft in rows and from the toptobottom collumns, the number of the [itex]b[/itex]s (in this case) must be less or equal to the number of [itex]a[/itex]'s.
For example that's not the case for any of my graphs execpt for the [itex]15[/itex].
[itex] \bar{3} \otimes \bar{3} [/itex]
The problem is that I end up with:
[itex] \bar{3} \otimes \bar{3} = 15 \oplus 6 \oplus 3 \oplus 3 [/itex]
Is that correct? It doesn't seem correct at all (dimensionally speaking I should have taken something like [itex]\bar{6} \oplus 3[/itex]  like baring the [itex]3 \otimes 3 =6 \oplus \bar{3}[/itex])...
In fact I am unable to understand the rule that says:
looking from the righttoleft in rows and from the toptobottom collumns, the number of the [itex]b[/itex]s (in this case) must be less or equal to the number of [itex]a[/itex]'s.
For example that's not the case for any of my graphs execpt for the [itex]15[/itex].
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