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Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 1, Pages 22–32 (Mi faa2887)  

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

Integral Models of Representations of Current Groups

A. M. Vershika, M. I. Graevb

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

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

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

Full text: PDF file (227 kB)
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English version:
Functional Analysis and Its Applications, 2008, 42:1, 19–27

Bibliographic databases:

UDC: 517.5
Received: 03.09.2007

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

    This publication is cited in the following articles:
    1. A. M. Vershik, “Does There Exist a Lebesgue Measure in the Infinite-Dimensional Space?”, Proc. Steklov Inst. Math., 259 (2007), 248–272  mathnet  crossref  mathscinet  zmath  elib  elib
    2. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Vershik A.M., “Invariant measures for the continual Cartan subgroup”, J. Funct. Anal., 255:9 (2008), 2661–2682  crossref  mathscinet  zmath  isi  elib
    4. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. 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  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    6. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. 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  mathnet  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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