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Mat. Sb. (N.S.), 1986, Volume 130(172), Number 2(6), Pages 131–150 (Mi msb1860)  

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

A complete classification of the representations of $\mathrm{GL}(\infty)$ containing the identity representation of the unitary subgroup

N. I. Nessonov


Abstract: It is proved that a previously known list of indecomposable spherical functions of the group $\mathrm{GL}(\infty)$ that are bilaterally invariant with respect to the unitary subgroup is complete.
Bibliography: 9 titles.

Full text: PDF file (983 kB)
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English version:
Mathematics of the USSR-Sbornik, 1987, 58:1, 127–147

Bibliographic databases:

UDC: 512
MSC: Primary 22D10; Secondary 22D25, 46L35
Received: 11.02.1985

Citation: N. I. Nessonov, “A complete classification of the representations of $\mathrm{GL}(\infty)$ containing the identity representation of the unitary subgroup”, Mat. Sb. (N.S.), 130(172):2(6) (1986), 131–150; Math. USSR-Sb., 58:1 (1987), 127–147

Citation in format AMSBIB
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\by N.~I.~Nessonov
\paper A~complete classification of the representations of $\mathrm{GL}(\infty)$ containing the identity representation of the unitary subgroup
\jour Mat. Sb. (N.S.)
\yr 1986
\vol 130(172)
\issue 2(6)
\pages 131--150
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=854968}
\zmath{https://zbmath.org/?q=an:0623.22017|0614.22007}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 58
\issue 1
\pages 127--147
\crossref{https://doi.org/10.1070/SM1987v058n01ABEH003096}
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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. G. I. Olshanskii, “Unitary representations of the group $SO_0(\infty,\infty)$ as limits of unitary representations of the groups $SO_0(n,\infty)$ as $n\to\infty$”, Funct. Anal. Appl., 20:4 (1986), 292–301  mathnet  crossref  mathscinet  zmath  isi
    2. G. I. Olshanskii, “Method of holomorphic extensions in the theory of unitary representations of infinite-dimensional classical groups”, Funct. Anal. Appl., 22:4 (1988), 273–285  mathnet  crossref  mathscinet  zmath  isi
    3. N. I. Nessonov, “On the decay of step for the Korteweg–de Vries–Burgers equation”, Funct. Anal. Appl., 26:2 (1992), 148–151  mathnet  crossref  mathscinet  zmath  isi
    4. A. Okounkov, “On representations of the infinite symmetric group”, Journal of Mathematical Sciences (New York), 96:5 (1999), 3550  crossref  mathscinet
    5. Borodin A., Olshanski G., “Representation Theory and Random Point Processes”, European Congress of Mathematics, ed. Laptev A., Eur. Math. Soc., 2005, 73–94  crossref  mathscinet  zmath  isi
    6. N. I. Nessonov, “Representations of $\mathfrak{S}_\infty$ admissible with respect to Young subgroups”, Sb. Math., 203:3 (2012), 424–458  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Bufetov A.I. Qiu Ya., “Ergodic Measures on Spaces of Infinite Matrices Over Non-Archimedean Locally Compact Fields”, Compos. Math., 153:12 (2017), 2482–2533  crossref  mathscinet  zmath  isi  scopus
    8. N. I. Nessonov, “Kharaktery beskonechnoi simmetricheskoi inversnoi polugruppy”, Funkts. analiz i ego pril., 54:3 (2020), 38–47  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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