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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?