Group representation theory MOC

Dual representation

Let be a Group representation. The dual representation is a representation carried by the dual vector space defined by rep

In the case of a unitary representation , the dual representation may be identified with the complex conjugate.

Functorial construction

The representation may be conceived as a functor from a groups-as-category . We have two contravariant functors and . The dual representation is thus the covariant functor

A representation is called self-dual iff it is equivalent to its dual , and a group representation is self-dual iff it preserves a nondegenerate bilinear form.

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