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.
@article{FAA_2012_46_1_a0,
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},
pages = {1--12},
publisher = {mathdoc},
volume = {46},
number = {1},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a0/}
}
TY - JOUR AU - A. M. Vershik AU - M. I. Graev TI - 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 JO - Funkcionalʹnyj analiz i ego priloženiâ PY - 2012 SP - 1 EP - 12 VL - 46 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a0/ LA - ru ID - FAA_2012_46_1_a0 ER -
%0 Journal Article %A A. M. Vershik %A M. I. Graev %T 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 %J Funkcionalʹnyj analiz i ego priloženiâ %D 2012 %P 1-12 %V 46 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a0/ %G ru %F FAA_2012_46_1_a0
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/