Editing Complex representation

{{distinguish|Complex envelope}}
In [[mathematics]], a '''complex representation''' is a [[group representation|representation]] of a [[Group (mathematics)|group]] (or [[Lie algebra representation|that]] of [[Lie algebra]]) on a complex vector space. Sometimes (for example in physics), the term '''complex representation''' is reserved for a representation on a complex vector space that is neither [[real representation|real]] nor [[pseudoreal representation|pseudoreal]] (quaternionic). 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 compact groups, the [[Frobenius-Schur indicator]] can be used to tell whether a representation is real, complex, or pseudo-real. 

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]].

== References ==
*{{Fulton-Harris}}

[[Category:Representation theory of groups]]