Find the number of inequivalent two-dimensional complex representations of the group $Z_4$
Any hints will be greatly appreciated. Thank you all
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Sign up to join this communityFind the number of inequivalent two-dimensional complex representations of the group $Z_4$
Any hints will be greatly appreciated. Thank you all
Hint: Using Maschke's Theorem, any such two-dimensional representation of $\mathbb{Z}_4$ is the direct sum of irreducible representations of $\mathbb{Z}_4$. You need to find the irreducible representations of the group (which all turn out to be one-dimensional because the group is abelian). Thus, any two-dimensional representation is the sum of two of these irreducible representations. The question then becomes a combinatorial one: how many ways can you choose two irreducible representations?