Abstract
The second error is more fundamental and is concerned with the case when one, or more, of the magnetic little groups Mk turns out to be unitary. We use the same notation as in APCI. Bradley and Davies2> have shown that an irreducible corepresentation of M induced from a small representation of a unitary magnetic little group Mk always belongs to case (c), i.e. when restricted to elements of the unitary space group G, the irreducible corepresentation DJ (or DJ) of M consists of two inequivalent irreducible representations J, J of G of the same dimension. In this case, there is always a doubling of degeneracy on introducing the antiunitary operators to form M. Thus, whenever an irreducible corepresentation of M arises, that is induced from a small representation of a unitary magnetic little group Mk, then it always belongs to case (c) and not to case (a) as suggested in APCI. If we want to evaluate the coefficients diJ,k in the reduction of the inner Kronecker product of two irreducible corepresentations DJi and DJJ into a sum of irreducible corepresentations DJk, viz:
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