The term complex representation has slightly different meanings in mathematics and physics.
In mathematics, a complex representation is a group representation of a group (or Lie algebra) on a complex vector space.
In physics, a complex representation is a group representation of a group (or Lie algebra) on a complex vector space 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 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.
Famous quotes containing the word complex:
“We must open our eyes and see that modern civilization has become so complex and the lives of civilized men so interwoven with the lives of other men in other countries as to make it impossible to be in this world and out of it.”
—Franklin D. Roosevelt (1882–1945)