Group representations in indefinite metric spaces

A group G of symmetry transformations of the rays of an indefinite metric space V with metric operator eta leads to a projective representation U of G in V in terms of eta-unitary, eta-antiunitary, eta-pseudounitary, and eta-pseudoantiunitary operators. We investigate the restrictions which are put on the irreducible components of U by the metric, and examine to what extent it is possible to decompose V into a direct sum of indefinite metric spaces, each carrying a projective representation of G. Attention is restricted to the cases where the subgroup of G which is represented by eta-unitary operators is of index 1 or 2.