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Let $G$ be a finite group with $|G|=n$, let $S_G=S_n$ be the group of $n!$ permutations of the set $G$. Then $G$ is a subgroup of $S_G$ via left-translation (i.e. $g\in G$ corresponds to the ...

Let $G$ be a finite group, $H$ a subgroup of $G$ and $g \in G$. Define $$ [gH] = \sum_{h \in H} gh, $$ viewed an element in the group algebra $\mathbb{C}[G]$. Given an irreducible character $\chi$ of $...

Let $H$ be the subgroup of the symmetric group $\mathfrak{S}_n$. Let $W_n$ be the group algebra of the hyperoctahedral group $\mathbb{Z}/2\mathbb{Z} \wr \mathfrak{S}_n$.The induced module $M:=\mathrm{...