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 $𝐺$ equals the order $| 𝐺 |$ of the group. rep

\sum 𝛾 \in ˆ 𝐺 (𝑑 𝛾) 2 = | 𝐺 |

Corollary

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

𝑍 (𝐺) = 𝐺 ⟹ ∣ ˆ 𝐺 ∣ = | 𝐺 |

tidy | en | SemBr

Table of Contents

Square sum of irrep dimensions

Corollary

Graph View

Backlinks