Obtaining the decuplet of baryon states from one state

[Xico Sim]

Hi, guys.

If you are given one state of the baryon decuplet (the upper-right state $\Deltaˆ{++}=uuu$, for instance), you can use the ladder operators to get the other states of the decuplet.
When I apply $T_-$ to uuu and normalizing, I get $\frac{1}{\sqrt{3}}(duu+udu+uud)$. However, in the decuplet I see $\Deltaˆ+=uud$ instead of $\frac{1}{\sqrt{3}}(duu+udu+uud)$. Why?

 

[Orodruin]

Please give a reference to what you are reading.

 

[Xico Sim]

Thomson's book: Modern particle physics. vide figure 9.17 on page 235, for instance, and page 227 where he applies the ladder operators to get the states of the center of the meson octet. In my case, I want to get all the decuplet states from one using the ladder operators.

 

[Xico Sim]

Well, as I understand it now, people use $uud$ as written above as an abbreviation...