Infinite dimensional irreducibility

Irreducibility of the Koopman representations for the group GL0(2∞,R), acting on three infinite rows

In representation theory, harmonic analysis for locally compact groups relies on the existence of the Haar measure. This measure exists only if a group is locally compact. Despite the absence of the Haar measure, in this paper we construct representations of infinite dimensional non-locally compact groups. Namely, we construct an analog of quasi-regular representations by using infinite products of Gaussian measures.