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vote
1answer
120 views

Direct sum and tensor product of two representations of a group

Our lecturer gave us a hard exercice to go further in group theory (we stopped at group actions) : Let G be a group, V and W complex vector spaces and $\rho_1 : G \mapsto GL(V) $ be a group ...
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218 views

Help deriving that $\mathrm{sign} : S_n\to \{\pm 1\}$ is multiplicative

$\def\sign{\operatorname{sign}}$ For homework, I am trying to show that $\sign:S_n \to \{\pm 1\}$ is multiplicative, i.e. that for any permutations $\sigma_1,\sigma_2$ we have $$\sign(\sigma_1 ...