Permutation operator applied to antisymmetric combination

[cks]

Homework Statement

I can't really imagine how this was approached.

Let $$P_{\alpha0}$$ fixed

$$P_{a0}A=\frac{1}{N!}\sum_{\alpha}\epsilon_{\alpha}P_{\alpha0}P_{\alpha}=\frac{1}{N!}\epsilon_{\alpha0}\sum_{\alpha}\epsilon_{\beta}P_{\beta}=\epsilon_{\alpha0}A<br />$$

Homework Equations

The Attempt at a Solution

I can understand that $$P_{\alpha0}P_{\alpha} = P_{\beta}$$ is a new permutation operator.

$$P_{a0}A=\frac{1}{N!}\sum_{\alpha}\epsilon_{\alpha}P_{\alpha0}P_{\alpha}=\frac{1}{N!}\sum_{\alpha}\epsilon_{\alpha}P_{\beta}$$

 

[Hurkyl]

What do all of your symbols mean?