On unitary/antiunitary projective representations of groups

Abstract

Unitary/antiunitary projective representations of groups (i.e., projective representations of groups where unitary as well as antiunitary operators in a separable complex Hilbert space are considered) are studied in a systematic way. Particular emphasis is put on continuous unitary/antiunitary projective representations of a Polish group G. It is shown that every continuous unitary/antiunitary projective representation of G can be lifted to a Borel unitary/antiunitary multiplier representation of G (namely, to a representation “up to a factor” which is a Borel mapping) and that this, in turn, can be derived from a continuous unitary/antiunitary (ordinary) representation of a Polish group obtained from an extension of G by the multiplicative group of all complex numbers of absolute value 1.