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In mathematics, if G is a group and Π is a representation of it over the complex vector space V, then the complex conjugate representation Π is defined over the complex conjugate vector space V as follows:
Π is also a representation, as one may check explicitly.
If g is a real Lie algebra and π is a representation of it over the vector space V, then the conjugate representation π is defined over the conjugate vector space V as follows:
π is also a representation, as one may check explicitly.
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