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

Functional Analysis and Its Applications volume 45, pages 225–239 (2011)Cite this article

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\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.

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Authors and Affiliations

  1. University of Vienna, Vienna, Austria

    Yu. A. Neretin

  2. Institute for Theoretical and Experimental Physics, Moscow State University, Moscow, Russia

    Yu. A. Neretin

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  1. Yu. A. Neretin
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Correspondence to Yu. A. Neretin.

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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 45, No. 3, pp. 79–96, 2011

Original Russian Text Copyright © by Yu. A. Neretin

To the memory of V. I. Arnold

Supported by FWF grant no. P22122.

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Neretin, Y.A. Sphericity and multiplication of double cosets for infinite-dimensional classical groups. Funct Anal Its Appl 45, 225–239 (2011). https://doi.org/10.1007/s10688-011-0025-6

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  • DOI: https://doi.org/10.1007/s10688-011-0025-6

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