What I am trying to do?
Work out the irreducible representation of the group element $(1,3,5) \in S_5$ for the partition $2+2+1$ .
Learn how to calculate irreducible representation from Young tableaux.
Partitions and Young tableaux:
Now I pick the partition $2+2+1$ and work out the representation of the group element $(1,3,5) \in S_5$.
First I work out the standard Young tableaux for the shape $2+2+1$.
Now I compute the Specht polynomials for each of the tableau.
Now I compute the representation for the permutation $\left(1, 3, 5\right) \in S_5$.
So, the irreducible representation of $\left(1, 3, 5\right)$ is :
My question: Am I doing it right?