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Funktsional. Anal. i Prilozhen., 2010, Volume 44, Issue 2, Pages 14–32 (Mi faa2983)  

This article is cited in 4 scientific papers (total in 4 papers)

Disjointness of representations arising in harmonic analysis on the infinite-dimensional unitary group

V. E. Gorinab

a M. V. Lomonosov Moscow State University
b Independent University of Moscow

Abstract: We prove the pairwise disjointness of representations $T_{z,w}$ of the infinite-dimensional unitary group. These representations are a natural generalization of the regular representation to the “big” group $U(\infty)$. They were introduced and studied by G. Olshanski and A. Borodin. The disjointness of these representations reduces to that of certain probability measures on the space of paths in the Gelfand–Tsetlin graph. We prove the latter disjointness using probabilistic and combinatorial methods.

Keywords: disjointness of representations, central measure, harmonic analysis, infinite-dimensional unitary group

DOI: https://doi.org/10.4213/faa2983

Full text: PDF file (290 kB)
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English version:
Functional Analysis and Its Applications, 2010, 44:2, 92–105

Bibliographic databases:

UDC: 519.21+512.547
Received: 10.10.2008

Citation: V. E. Gorin, “Disjointness of representations arising in harmonic analysis on the infinite-dimensional unitary group”, Funktsional. Anal. i Prilozhen., 44:2 (2010), 14–32; Funct. Anal. Appl., 44:2 (2010), 92–105

Citation in format AMSBIB
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\paper Disjointness of representations arising in harmonic analysis on the infinite-dimensional unitary group
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\pages 14--32
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\issue 2
\pages 92--105
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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. A. Osinenko, “Harmonic analysis on the infinite-dimensional unitary group”, J. Math. Sci. (N. Y.), 181:6 (2012), 886–913  mathnet  crossref
    2. A. Osinenko, “Harmonic analysis on the infinite-dimensional unitary-symplectic group”, J. Math. Sci. (N. Y.), 190:3 (2013), 472–485  mathnet  crossref  mathscinet
    3. Alexei Borodin, Grigori Olshanski, “The Young bouquet and its boundary”, Mosc. Math. J., 13:2 (2013), 193–232  mathnet  crossref  mathscinet
    4. Olshanski G., “Markov Dynamics on the Dual Object To the Infinite-Dimensional Unitary Group”, Probability and Statistical Physics in St. Petersburg, Proceedings of Symposia in Pure Mathematics, 91, eds. Sidoravicius V., Smirnov S., Amer Mathematical Soc, 2016, 373–394  crossref  mathscinet  zmath  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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