Group character

Character table

The character table of a group is a square¹ matrix where each column is labeled by conjugacy class and each row by an Irrep. Let label irreps and label conjugacy classes . Then for all .

(trivial)

Properties characterising the character table, and thereby useful for determining its entries, include the Square sum of irrep dimensions and the Orthonormality of irreducible characters, which gives

we also have

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tidy | en | sembr

Footnotes

1. Since The number of conjugacy classes equals the number of non-equivalent irreps of a group. ↩