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A Remark on the Orthogonality Relations in the Representation Theory of Finite Groups
Published online by Cambridge University Press: 20 November 2018
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Let G be a finite group of order g, and
be an absolutely irreducible representation of degree fμ over a field of characteristic zero. As is well known, by using Schur's lemma (1), we can prove the following orthogonality relations for the coefficients :
1
It is easy to conclude from (1) the following orthogonality relations for characters:
where
and is 1 or 0 according as t and s are conjugate in G or not, and n(t) is the order of the normalize of t.
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