Geodesic
Special Representations of the Groups $U(\infty,1)$ and $O(\infty,1)$ and the Associated Representations of the Current Groups $U(\infty,1)^X$ and $O(\infty,1)^X$ in Quasi-Poisson Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 1-12

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A method for constructing representations of the current groups $O(n,1)^X$ and $U(n,1)^X$, $n\in\mathbb N$, developed in the previous papers by the authors is generalized to the case of infinite $n$. This leads to an interesting difference in construction (absent for finite $n$) between the cases of the orthogonal and unitary groups, which is due to the different character of special representations of the groups of coefficients.
Keywords: current group, integral model, Fock representation, canonical representation, special representation, infinite-dimensional Lebesgue measure. 
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     author = {A. M. Vershik and M. I. Graev},
     title = {Special {Representations} of the {Groups} $U(\infty,1)$ and $O(\infty,1)$ and the {Associated} {Representations} of the {Current} {Groups} $U(\infty,1)^X$ and $O(\infty,1)^X$ in {Quasi-Poisson} {Spaces}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a0/}
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A. M. Vershik; M. I. Graev. Special Representations of the Groups $U(\infty,1)$ and $O(\infty,1)$ and the Associated Representations of the Current Groups $U(\infty,1)^X$ and $O(\infty,1)^X$ in Quasi-Poisson Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 1-12. http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a0/