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user 1921
For questions about the algebraic concept of 'character': a function from a group into a field satisfying certain properties. Not to be confused with the more commonly known psychological term.
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Proving interesting theorems about S_n using its character table.
For symmetric groups, there is a third nice basis: For $\lambda \vdash n$, let $$ S_\lambda = \prod_{i=1}^{n} S_i^{\lambda_i} $$ and consider the characters of the induced reps $Ind_{S_\lambda}^{S_n} \ … Consider the change of basis matrix relating characters of induces reps and characters of irreps: Knowing how character theory for symmetric groups works over $\mathbb{Z}$ (i.e., that both span integrally …
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