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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
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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
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/faa3042https://doi.org/10.4213/faa3042 http://mi.mathnet.ru/eng/faa/v45/i3/p79
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:
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Yu. Neretin, “Symmetries of Gaussian measures and operator colligations”, J. Funct. Anal., 263:3 (2012), 782–802
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Yu. A. Neretin, “The space $L^2$ on semi-infinite Grassmannian over finite field”, Adv. Math., 250 (2014), 320–350
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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
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Yu. A. Neretin, “Infinite symmetric groups and combinatorial constructions of topological field theory type”, Russian Math. Surveys, 70:4 (2015), 715–773
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Yu. A. Neretin, “Several remarks on groups of automorphisms of free groups”, J. Math. Sci. (N. Y.), 215:6 (2016), 748–754
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Neretin Yu.A., “Hua-Type Beta-Integrals and Projective Systems of Measures on Flag Spaces”, Int. Math. Res. Notices, 2015, no. 21, 11289–11301
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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
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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
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Yu. A. Neretin, “Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument”, Funct. Anal. Appl., 51:2 (2017), 98–111
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Pablo Gonzalez Pagotto, “A Product on Double Cosets of $B_\infty$”, SIGMA, 14 (2018), 134, 18 pp.
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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
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