# Questions tagged [characters]

For questions about characters (traces of representations of a group on a vector space).

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### Orthogonality relations for matrix elements of irreducible representations

I am reading Howard Georgi's "Lie Algebras in Particle Physics" and have a question concerning the presented orthogonality relations for matrix elements of irreducible representations. To ...
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### Intuitions behind Frobenius' generalization of characters to nonabelian finite group given the historical context

I'm reading about the history of character theory of finite group, especially about the invention of character theory by Frobenius. According to most of the related papers (e.g. Pioneers of ...
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### About homogenous completely irreducible module

I'm stuck on something, I'd appreciate it if you could help :) Let $A$ be a $F$-algebra, $V$ be a completely reducible $A$-module and $M$ is an irreducible $A$- module. Now let's consider $M(V)$, ...
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### The character table of an abelian group

I am attempting to construct the character table for $\mathbb{Z}_8$. I know a few things off the bat: Since $\mathbb{Z}_8$ is abelian, its conjugacy classes are singletons (i.e. we have eight classes)...
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Let ($χ,V$) be a irreducible representation and $h$ be class function. Then, why $\sum_{g∈G}\overline {h(g)}χ_v(g)$ is scalar of identity map of $V$ ? (I try to prove find the relation between $\sum_{... 2 votes 1 answer 50 views ### Compute character table of$S_4$in Fulton-Harris This is an example in Fulton-Harris 2.3 at p.g. 18: computing the character table of$S_4$. I have computed$\chi_{trivial},\chi_{sgn},\chi_{std},\chi_{std\cdot sgn}$. The last character, denoted as$\...
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Suppose $G$ is a finite cyclic group, and let $\chi: G \to \mathbb{C}^*$ be a character of order $n$. That is, $\chi^n$ is the identity homomorphism. I came across the following relation in a paper ...