Irreducible group action

Irreducible actions of the group GL(∞) on L²-spaces on 3 infinite rows

Compared with groups of finite dimension, the theory of infinite-dimensional Lie groups is poorly developed. We construct the unitary representation of an infinite-dimensional general linear group and establish its irreducibility. The proof is based on the corresponding von Neumann algebra, our previous work on the properties of infinite parallelotopes and the properties of generalized characteristic polynomials.