M.I. Graev, A.M. Vershik
The Basic Representation of the Current Group $O(n,1)^X$ in the $L^2$ Space over the Generalized Lebesgue Measure
Preprint series: ESI preprints

MSC:

43A65 Representations of groups, semigroups, etc., See Also {22A10, 22A20, 22Dxx, 22E45}

22E46 Semisimple Lie groups and their representations

17B65 Infinite-dimensional Lie algebras, See also {22E65}

Abstract: We gave a new model of the irreducible unitary representation
of the current group with values in the group $O(n,1)$. The realization
is given in the space $L^2$ over infinite dimensional
analog of Lesbegue measure.
Keywords: current groups, canonical state, special representation