# Questions tagged [character-theory]

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### How to know the character table of the twisted group algebra of the symmetric group $S_4$

Given the character table of its Schur cover group, is there a way to obtain the character table of twisted group algebra from that? I am particularly interested in the symmetric group $S_4$.
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### New characters from old

(All groups in the following discussion are assumed to be finite.) Character induction is an operation that produces a character of a group given a character of a subgroup. I'm aware that there are ...
• 1,215
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### An arithmetic problem involving a system of equations

Fix a positive integer $r$. Describe the solutions to the system of equations given by: $$$$\sum_{1\leq i\leq r}X_i^2\equiv0\pmod{X_k}(1\leq k\leq r)$$$$ Example: In the case ...
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### Representations of finite groups over the "field with one element"

Have there been any attempts to extend the "F_un" analogy to the representation theory of finite groups? If I might be allowed some speculation: If combinatorics can be regarded as analagous ...
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I know the following fact: If $G$ is an abelian group and $S\subset G$ be a subset of G such that $1\notin G$ and $S=S^{-1}$ and we draw an edge between $g$ and $h$ if and only if $hg^{-1}\in S$,then ...