Corepresentations of unitary and antiunitary groups

Not to be confused with comodule which also uses the term corepresentation.

In quantum mechanics, symmetry operations are of importance in giving information about solutions to a system. Typically these operations form a mathematical group, such as the rotation group SO(3) for spherically symmetric potentials. The representation theory of these groups leads to irreducible representations, which for SO(3) gives the angular momentum ket vectors of the system.

Standard representation theory uses linear operators. However, some operators of physical importance such as time reversal are antilinear, and including these in the symmetry group leads to groups including both unitary and antiunitary operators.

This article is about corepresentation theory, the equivalent of representation theory for these groups. It is mainly used in the theoretical study of magnetic structure but is also relevant to particle physics due to CPT symmetry. It gives basic results, the relation to ordinary representation theory and some references to applications.