Complex representation
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In mathematics, a complex representation is a group representation that is neither real nor pseudoreal. In other words, the group elements are expressed as complex matrices, and the complex conjugate of a complex representation is a different, non-equivalent representation.
For example, the N-dimensional fundamental representation of SU(N) for N greater than two is a complex representation whose complex conjugate is often called the antifundamental representation.
A representation of a group by roots of unity is called the character group.