Geodesic
A Commutative Model of a Representation of the Group $O(n,1)^X$ and a Generalized Lebesgue Measure in the Space of Distributions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 2, pp. 1-12

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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.
Keywords: current group, basic representation, commutative model.
Mots-clés : orthogonal group 
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     title = {A {Commutative} {Model} of a {Representation} of the {Group} $O(n,1)^X$ and a {Generalized} {Lebesgue} {Measure} in the {Space} of {Distributions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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A. M. Vershik; M. I. Graev. A Commutative Model of a Representation of the Group $O(n,1)^X$ and a Generalized Lebesgue Measure in the Space of Distributions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 2, pp. 1-12. http://geodesic.mathdoc.fr/item/FAA_2005_39_2_a0/