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Funktsional. Anal. i Prilozhen., 2005, Volume 39, Issue 2, Pages 1–12 (Mi faa36)  

This article is cited in 8 scientific papers (total in 10 papers)

A Commutative Model of a Representation of the Group $O(n,1)^X$ and a Generalized Lebesgue Measure in the Space of Distributions

A. M. Vershikab, M. I. Graevc

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b International Erwin Schrödinger Institute for Mathematical Physics
c Scientific Research Institute for System Studies of RAS

Abstract: For an irreducible unitary representation of an $O(n,1)$ current group, we consider a commutative model obtained by diagonalization with respect to a maximal unipotent subgroup. This model leads to a new measure on the space of distributions. The measure is invariant with respect to an infinite-dimensional linear symmetry group.

Keywords: current group, orthogonal group, basic representation, commutative model

DOI: https://doi.org/10.4213/faa36

Full text: PDF file (222 kB)
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English version:
Functional Analysis and Its Applications, 2005, 39:2, 81–90

Bibliographic databases:

UDC: 517.5
Received: 17.01.2005

Citation: A. M. Vershik, M. I. Graev, “A Commutative Model of a Representation of the Group $O(n,1)^X$ and a Generalized Lebesgue Measure in the Space of Distributions”, Funktsional. Anal. i Prilozhen., 39:2 (2005), 1–12; Funct. Anal. Appl., 39:2 (2005), 81–90

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Vershik, “On F. A. Berezin and his work on representations of current groups”, J. Math. Sci. (N. Y.), 141:4 (2007), 1385–1389  mathnet  crossref  mathscinet  zmath  elib
    2. A. M. Vershik, M. I. Graev, “Structure of the complementary series and special representations of the groups $O(n,1)$ and $U(n,1)$”, Russian Math. Surveys, 61:5 (2006), 799–884  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. 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
    4. 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
    5. A. M. Vershik, I. M. Gel'fand, S. G. Gindikin, A. A. Kirillov, G. L. Litvinov, V. F. Molchanov, Yu. A. Neretin, V. S. Retakh, “Mark Iosifovich Graev (to his 85th brithday)”, Russian Math. Surveys, 63:1 (2008), 173–188  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. 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
    7. 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
    8. A. M. Vershik, M. I. Graev, “Osobye predstavleniya grupp $U(\infty,1)$ i $O(\infty,1)$ i svyazannye s nimi predstavleniya grupp tokov $U(\infty,1)^X$ i $O(\infty,1)^X$ v kvazipuassonovom prostranstve”, Funkts. analiz i ego pril., 46:1 (2012), 1–12  mathnet  crossref  mathscinet  zmath  elib
    9. 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
    10. 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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