Representation theory MOC

Square sum of irrep dimensions

As an immediate consequence of orthogonality of irreps, it follows that the square sum of the dimensions of all (non-equivalent) irreps of a finite group equals the order of the group. rep

Corollary

Since Irreps of abelian groups are 1-dimensional, it follows that the number of irreps of an abelian group equals the order of the group . rep

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