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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
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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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This publication is cited in the following articles:
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A. A. Osinenko, “Harmonic analysis on the infinite-dimensional unitary group”, J. Math. Sci. (N. Y.), 181:6 (2012), 886–913
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A. Osinenko, “Harmonic analysis on the infinite-dimensional unitary-symplectic group”, J. Math. Sci. (N. Y.), 190:3 (2013), 472–485
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Alexei Borodin, Grigori Olshanski, “The Young bouquet and its boundary”, Mosc. Math. J., 13:2 (2013), 193–232
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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
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