  We 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,\nu) of functionals on the
the space F of the generalized functions on the manifold X which are square
integrable over measure \nu which 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 \nu
is 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).
