Infinite dimensional irreducibility
Representation theory
Irreducibility of the Koopman representations for the group GL0(2∞,R), acting on three infinite rows
Submitted to Journal of Functional Analysis (2023)
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.
Submitted to Journal of Functional Analysis (2023)