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In quantum mechanics, symmetry operations are of importance ingiving information about solutions to a system.Typically these operations form a mathematicalgroup, such as the rotationgroup SO for spherically symmetric potentials.The representation theory of these groups leads to irreducible representations, which for SO gives the angular momentumket vectors of the system.
Standard representation theory useslinear operators. However, some operatorsof physical importance such as time reversal areantilinear,and including these in the symmetry group leads to groupsincluding both unitary and antiunitary operators.
This article is about corepresentation theory, the equivalent ofrepresentation theory for these groups. It is mainly used in the theoreticalstudy of magnetic structure but is also relevant toparticle physics due to CPT symmetry.It gives basic results, the relation to ordinary representation theory and some references to applications.