On irreducible corepresentations of finite magnetic groups

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Abstract
We have obtained a set of homogeneous linear equations in the Clebsch‐Gordan coefficients for the Kronecker inner direct product of two irreducible corepresentations of a finite magnetic group. The solutions of these equations give the Clebsch‐Gordan coefficients even when the group is not simply reducible. The nontrivial Clebsch‐Gordan coefficients for the magnetic group C4ν(C2ν) have been evaluated. We have also investigated the criterion determining whether a particular irreducible corepresentation is equivalent to its complex conjugate representation. A projection operator has been constructed for obtaining the basis pertaining to a particular irreducible corepresentation.

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