Abstract
One starts with a representation of a given abstract group G=H+sH (where H is its subgroup of index 2, and s is a coset representative) by a group of unitary and antiunitary operators in the state space of a quantum system. Co-representation theory maps further these operators into matrices, which are linear operators in the space Cn of number columns, but it fails to preserve homomorphism. An equivalent theory in terms of unitary matrices and antimatrices (antilinear operators in Cn) which is based on isomorphism with the mentioned group of operators is presented. The connection (subduction of the one side and *-induction on the other) between the set of all unitary irreducible matrix representations of H and the set of all unitary irreducible matrix-antimatrix representations of G are studied. Finally, a simple construction of the latter from the former is given.
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