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Funktsional. Anal. i Prilozhen., 2011, Volume 45, Issue 3, Pages 79–96 (Mi faa3042)  

This article is cited in 11 scientific papers (total in 11 papers)

Sphericity and multiplication of double cosets for infinite-dimensional classical groups

Yu. A. Neretinabc

a University of Vienna
b Institute for Theoretical and Experimental Physics
c Moscow State University

Abstract: We construct spherical subgroups in infinite-dimensional classical groups $G$ (usually they are not symmetric and their finite-dimensional analogs are not spherical). We present a structure of a semigroup on double cosets $L\setminus G/L$ for various subgroups $L$ in $G$; these semigroups act in spaces of $L$-fixed vectors in unitary representations of $G$. We also obtain semigroup envelops of groups $G$ generalizing constructions of operator colligations.

Keywords: spherical subgroup, spherical function, unitary representation, operator colligation, characteristic function (transfer function), category representation, inner function.

DOI: https://doi.org/10.4213/faa3042

Full text: PDF file (295 kB)
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English version:
Functional Analysis and Its Applications, 2011, 45:3, 225–239

Bibliographic databases:

UDC: 517.986.4+512.58+517.984.4+512.546.4
Received: 24.01.2011

Citation: Yu. A. Neretin, “Sphericity and multiplication of double cosets for infinite-dimensional classical groups”, Funktsional. Anal. i Prilozhen., 45:3 (2011), 79–96; Funct. Anal. Appl., 45:3 (2011), 225–239

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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. Yu. Neretin, “Symmetries of Gaussian measures and operator colligations”, J. Funct. Anal., 263:3 (2012), 782–802  crossref  mathscinet  zmath  isi  elib  scopus
    2. Yu. A. Neretin, “The space $L^2$ on semi-infinite Grassmannian over finite field”, Adv. Math., 250 (2014), 320–350  crossref  mathscinet  zmath  isi  elib  scopus
    3. Yu. A. Neretin, “Infinite-dimensional $p$-adic groups, semigroups of double cosets, and inner functions on Bruhat–Tits buildings”, Izv. Math., 79:3 (2015), 512–553  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Yu. A. Neretin, “Infinite symmetric groups and combinatorial constructions of topological field theory type”, Russian Math. Surveys, 70:4 (2015), 715–773  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Yu. A. Neretin, “Several remarks on groups of automorphisms of free groups”, J. Math. Sci. (N. Y.), 215:6 (2016), 748–754  mathnet  crossref  mathscinet
    6. Neretin Yu.A., “Hua-Type Beta-Integrals and Projective Systems of Measures on Flag Spaces”, Int. Math. Res. Notices, 2015, no. 21, 11289–11301  crossref  mathscinet  zmath  isi  scopus
    7. Yu. A. Neretin, “Radial parts of Haar measures and probability distributions on the space of rational matrix-valued functions”, Izv. Math., 80:6 (2016), 1118–1130  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. Neretin Yu.A., “On P-Adic Colligations and ‘Rational Maps’ of Bruhat-Tits Trees”, Geometric Methods in Physics, Trends in Mathematics, ed. Kielanowski P. Ali S. Bieliavsky P. Odzijewicz A. Schlichenmaier M. Voronov T., Springer Int Publishing Ag, 2016, 139–158  crossref  mathscinet  zmath  isi
    9. Yu. A. Neretin, “Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument”, Funct. Anal. Appl., 51:2 (2017), 98–111  mathnet  crossref  crossref  isi  elib
    10. Pablo Gonzalez Pagotto, “A Product on Double Cosets of $B_\infty$”, SIGMA, 14 (2018), 134, 18 pp.  mathnet  crossref
    11. Y. A. Neretin, “On the group of infinite $p$-adic matrices with integer elements”, Teoriya predstavlenii, dinamicheskie sistemy, kombinatornye metody. XXIX, Zap. nauchn. sem. POMI, 468, POMI, SPb., 2018, 105–125  mathnet
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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