A Commutative Model of a Representation of the Group $O(n,1)^X$ and a Generalized Lebesgue Measure in the Space of Distributions

For an irreducible unitary representation of an $O(n,1)$ current group, we consider a commutative model obtained by diagonalization with respect to a maximal unipotent subgroup. This model leads to a new measure on the space of distributions. The measure is invariant with respect to an infinite-dimensional linear symmetry group.