Representations of symetric group S3 (sorry in advance for my english. Im not sure my terminology is correct)
I'm trying to solve a problem:
Let $e_1$ , $e_2$ , $e_3$ be a base of $C^3$ (3-D vectors with complex elements). Let $A(g)e_i=e_{g(i)}$ be a representation of the symmetric group $S_3$ ($g\in S_3$). 
Also let $V=\{z_1,z_2,z_3\in C^3|z_1+z_2+z_3=0\}$ a subspace of $C^2$. 
The question here is to find the restriction ($P(g)$) of $A(g)$ at the subspace $V$, but i don't understand what this means.

Since $V$ is an invariant subspace of $\mathbb C^3$, $\rho(g)(v) \in V$ for every $v \in V$. Thus you have to compute the $2 \times 2$ matrix associated to every element $ g \in S_3$. 
