A new look at unitary-antiunitary representations of groups and their construction
Fedor Herbut, Milan Vujičić, Z. Papadopolos · Journal of Physics A Mathematical and General · 1980
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 C n of number columns, but it fails to preserve homomorphism. An equivalent theory in terms of unitary matrices and antimatrices (antilinear operators in C n ) 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.