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Orthogonal Group Representations


The term "orthogonal group representations" is used here for a pair of finite-dimensional group representations of a finite group G over the complex numbers whose characters chi_i and chi_j are orthogonal, i.e., satisfy

 sum_(g in G)chi_i(g)chi_j(g)^_=0.

The sum is over all elements of G. In particular, inequivalent irreducible representations have orthogonal characters with respect to this Hermitian inner product.


See also

Group, Group Character, Group Representation, Hermitian Inner Product, Irreducible Representation

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Cite this as:

Weisstein, Eric W. "Orthogonal Group Representations." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OrthogonalGroupRepresentations.html

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