All commutative groups have one dimensional representation(adsbygoogle = window.adsbygoogle || []).push({});

##D(g_i)=1, \forall i##

I understand what is representation. Also I know what is one, two... dimensional representation. But what is irreducible representation I do not understand. How you could have two dimensional irreducible representation of commutative group when you have always one dimensional one. Also you could have two two-dimensional representation of which one is reducible and one is irreducible. I'm confused with the concept of irreducible representation. If you have group ##G## of order ##ordG## with ##K## classes then if

##\sum_{i=1}^{K}n_i|\chi_i|^2=ordG##

group is irreducible. Otherwise is reducible. ##n_i## is number of elements in every class.

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# Irreducible representation. I'm confused.

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