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Special representations of the groups U(∞, 1) and O(∞, 1) and the associated representations of the current groups U(∞, 1)X and O(∞, 1)X in quasi-poisson spaces

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Abstract

A method for constructing representations of the current groups O(n, 1)X and U(n, 1)X, n ε ℕ, developed in the previous papers by the authors is generalized to the case of infinite n. This leads to an interesting difference in construction (absent for finite n) between the cases of the orthogonal and unitary groups, which is due to the different character of special representations of the groups of coefficients.

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Authors and Affiliations

  1. St. Petersburg Department of Steklov Institute of Mathematics, St. Petersburg, Russia

    A. M. Vershik

  2. Institute for System Studies, Moscow, Russia

    M. I. Graev

Authors
  1. A. M. Vershik
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  2. M. I. Graev
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Correspondence to A. M. Vershik.

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Translated from Funktsional’ nyi Analiz i Ego Prilozheniya, Vol. 46, No. 1, pp. 1–12, 2012

Original Russian Text Copyright © by A. M. Vershik and M. I. Graev

The first author is supported by RFBR grants nos. 11-01-00677a and 11-01-120192-ofi-m, the second author is supported by RFBR grant no. 10-01-00041a.

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Vershik, A.M., Graev, M.I. Special representations of the groups U(∞, 1) and O(∞, 1) and the associated representations of the current groups U(∞, 1)X and O(∞, 1)X in quasi-poisson spaces. Funct Anal Its Appl 46, 1–10 (2012). https://doi.org/10.1007/s10688-012-0001-9

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  • DOI: https://doi.org/10.1007/s10688-012-0001-9

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