Complex Representation

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:

    All propaganda or popularization involves a putting of the complex into the simple, but such a move is instantly deconstructive. For if the complex can be put into the simple, then it cannot be as complex as it seemed in the first place; and if the simple can be an adequate medium of such complexity, then it cannot after all be as simple as all that.
    Terry Eagleton (b. 1943)