New answers tagged characters
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Solution to system of nonlinear equations
If you multiply the fifth character with the second, you obtain another irreducible character. The remaining missing character should be easy to determine.
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Every irreducible character of $S_n$ is an integer valued function.
Personally I do not know how to do this without either Galois theory or the construction of the Specht modules. Here is the Galois theory argument, just to record it here. An element $g$ of a finite ...
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Every irreducible character of $S_n$ is an integer valued function.
I think the following can be a simple argument: one can prove that, for $G$ a finite group and $V$ a representation of $G$,
$$
\chi_{V^*}(g)=\overline{\chi_V}(g)=\chi_V\left(g^{-1}\right) \quad \...
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Why do characters fail to characterize non-abelian LCH-groups?
The short answer is that if $G$ is a group and $A$ an abelian group (like $\mathbb T$), then every group homomorphism $\phi\colon G\to A$ factors through the abelianization $G/[G,G]$. Here $[G,G]$ is ...
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