The Poisson model of the Fock space and representations of current groups

Vershik, A.; Graev, M.

doi:10.1090/S1061-0022-2012-01204-5

The Poisson model of the Fock space and representations of current groups
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by A. M. Vershik and M. I. Graev
Translated by: N. V. Tsilevich

St. Petersburg Math. J. 23 (2012), 459-510

DOI: https://doi.org/10.1090/S1061-0022-2012-01204-5

Published electronically: March 2, 2012

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Abstract:

The quasi-Poisson measures are considered, i.e., the $\sigma$-finite measures given by a density with respect to a Poisson measure. Representations of current groups are constructed in Hilbert spaces of functionals integrable with respect to a quasi-Poisson measure. For the groups $O(n,1)$ and $U(n,1)$, these models give new, more convenient, realizations of the representations in Fock spaces constructed in the previous papers by the authors. A crucial role in considerations is played by spaces of configurations and an analogy between quasi-Poisson and stable measures.

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