2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74558We give the realization of the representation of the current group O(n,1)^X where X is a manifold, in the Hilbert space of L^2(F,ν) of functionals on the the space F of the generalized functions on the manifold X which are square integrable over measure νwhich is related to a distinguish Levy process with values in R^{n-1} which generalized one dimensional gamma process. Unipotent subgroup of the group O(n,1)^X acts as the group of multiplicators. Measure νis sigma-finite and invariant under the action current group O(n-1)^X. Ther case of n=2 (SL(2,R^X)) was considered before in the series of papers starting from the article Vershik-Gel'fand-Graev (1973).26 p. Refs 19Representation TheoryProbability22E45text