- #1

ChrisVer

Gold Member

- 3,380

- 461

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 right-to-left in rows and from the top-to-bottom 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 right-to-left in rows and from the top-to-bottom 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].

#### Attachments

Last edited: