A. M. Vershik, M. I. Graev, “Integral Models of Representations of Current Groups”, Funktsional. Anal. i Prilozhen., 42:1 (2008), 22–32; Funct. Anal. Appl., 42:1 (2008), 19

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Funktsional'nyi Analiz i ego Prilozheniya, 2008, Volume 42, Issue 1, Pages 22–32
DOI: https://doi.org/10.4213/faa2887 (Mi faa2887)

This article is cited in 7 scientific papers (total in 8 papers)

Integral Models of Representations of Current Groups

A. M. Vershik^a, M. I. Graev^b

^a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
^b Scientific Research Institute for System Studies of RAS

Full-text PDF (227 kB) Citations (8)

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DOI: https://doi.org/10.4213/faa2887

Abstract: We suggest a new construction of nonlocal representations of the current group. Instead of the Fock space, which is usually used in this situation, we consider the direct integral of countable tensor products of representations over the trajectories of some stochastic process. The construction substantially uses the invariance of the so-called infinite-dimensional Lebesgue measure.

Keywords: current group, summable representation, integral of tensor products.

Received: 03.09.2007

English version:
Functional Analysis and Its Applications, 2008, Volume 42, Issue 1, Pages 19–27
DOI: https://doi.org/10.1007/s10688-008-0002-x

Bibliographic databases:

Document Type: Article

UDC: 517.5

Language: Russian

Citation: A. M. Vershik, M. I. Graev, “Integral Models of Representations of Current Groups”, Funktsional. Anal. i Prilozhen., 42:1 (2008), 22–32; Funct. Anal. Appl., 42:1 (2008), 19–27

Citation in format AMSBIB

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https://doi.org/10.4213/faa2887

https://www.mathnet.ru/eng/faa/v42/i1/p22

This publication is cited in the following 8 articles:

A. M. Vershik, M. I. Graev, “Nonunitary representations of the groups of $U(p,q)$ -currents for $q\geq p>1$ ”, J. Math. Sci. (N. Y.), 232:2 (2018), 99–120
V. M. Buchstaber, M. I. Gordin, I. A. Ibragimov, V. A. Kaimanovich, A. A. Kirillov, A. A. Lodkin, S. P. Novikov, A. Yu. Okounkov, G. I. Olshanski, F. V. Petrov, Ya. G. Sinai, L. D. Faddeev, S. V. Fomin, N. V. Tsilevich, Yu. V. Yakubovich, “Anatolii Moiseevich Vershik (on his 80th birthday)”, Russian Math. Surveys, 69:1 (2014), 165–179
A. M. Vershik, M. I. Graev, “Cohomology in Nonunitary Representations of Semisimple Lie Groups (the Group $U(2,2)$ )”, Funct. Anal. Appl., 48:3 (2014), 155–165
A. M. Vershik, M. I. Graev, “Poisson model of the Fock space and representations of current groups”, St. Petersburg Math. J., 23:3 (2012), 459–510
A. M. Vershik, M. I. Graev, “Integral models of representations of the current groups of simple Lie groups”, Russian Math. Surveys, 64:2 (2009), 205–271
A. M. Vershik, M. I. Graev, “Integral Models of Unitary Representations of Current Groups with Values in Semidirect Products”, Funct. Anal. Appl., 42:4 (2008), 279–289
Vershik A.M., “Invariant measures for the continual Cartan subgroup”, J. Funct. Anal., 255:9 (2008), 2661–2682
A. M. Vershik, “Does There Exist a Lebesgue Measure in the Infinite-Dimensional Space?”, Proc. Steklov Inst. Math., 259 (2007), 248–272

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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