Skip to main content
SpringerLink
Log in

Unitary representations of the group SOo(∞, ∞) as limits of unitary representations of the groups SOo(n, ∞) as n → ∞

  • Published:
Functional Analysis and Its Applications Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. A. M. Vershik, "A description of invariant measures for actions of some infinite-dimensional groups," Dokl. Akad. Nauk SSSR,218, No. 4, 749–752 (1974).

    Google Scholar 

  2. A. M. Vershik and S. V. Kerov, "Asymptotic theory of characters of the symmetric group," Funkts. Anal. Prilozhen.,15, No. 4, 15–27 (1981).

    Google Scholar 

  3. A. M. Vershik and S. V. Kerov, "Characters and quotient representations of the infinite unitary group," Dokl. Akad. Nauk SSSR,267, No. 2, 272–276 (1982).

    Google Scholar 

  4. D. P. Zhelobenko, Compact Lie Groups and Their Representations [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  5. N. I. Nessonov, "A complete classification of representations of GL(∞) containing the identity representation of a unitary subgroup," Mat. Sb.,130, No. 1, 131–150 (1986).

    Google Scholar 

  6. G. I. Ol'shanskii, "Unitary representations of the infinite—dimensional classical groups U(p, ∞), SOo(p, ∞), Sp(p, ∞) and the corresponding groups of movements," Funkts. Anal. Prilozhen.,12, No. 3, 32–44 (1978).

    Google Scholar 

  7. G. I. Ol'shanskii, "A description of unitary representations with leading weight for the groups U(p, e)." Funkts. Anal. Prilozhen.,14, No. 3, 32–44 (1980).

    Google Scholar 

  8. G. I. Ol'shanskii, "A construction of unitary representations with leading weight for the groups," Dokl. Akad. Nauk SSSR,250, No. 2, 284–288 (1980).

    Google Scholar 

  9. G. I. Ol'shanskii, "Invariant cones in Lie algebras, Lie semigroups and a holomorphic discrete series, "Funkts. Anal. Prilozhen.,15, No. 4, 53–66 (1981).

    Google Scholar 

  10. G. I. Ol'shanskii, "Spherical functions and characters on the group U(∞)X," Usp. Mat. Nauk,37, No. 2, 217–218 (1982).

    Google Scholar 

  11. G. I. Ol'shanskii, "Unitary representations of infinite—dimensional pairs (G, K) and the formalism of R. How," Dokl. Akad. Nauk SSSR,269, No. 1, 33–36 (1983).

    Google Scholar 

  12. G. I. Ol'shanskii, "Infinite—dimensional classical groups of finite R—rank: a description of representations and asymptotic theory," Funkts. Anal. Prilozhen.,18, No. 1, 28–42 (1984).

    Google Scholar 

  13. G. I. Ol'shanskii, "Unitary representations of the infinite symmetric group: a semigroup approach," in: Representations of Lie Groups and Lie Algebras, Akademiai Kiado, Budapest (1985), pp. 181–197.

    Google Scholar 

  14. I. Herstein, Noncommutative Rings [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  15. R. C. King, "Branching rules for classical Lie groups using tensor and spinor methods," J. Phys. A. Math. Gen.,8, No. 4, 429–449 (1975).

    Google Scholar 

  16. S. Stratila and D. Voiculescu, Representations of AF-Algebras and of the Group U(∞), Lect. Notes Math.,486, Springer, Berlin (1975).

    Google Scholar 

Download references

Authors
  1. G. I. Ol'shanskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

VNIPIIStromsyr'e. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 20, No. 4, pp. 46–57, October–December, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ol'shanskii, G.I. Unitary representations of the group SOo(∞, ∞) as limits of unitary representations of the groups SOo(n, ∞) as n → ∞. Funct Anal Its Appl 20, 292–301 (1986). https://doi.org/10.1007/BF01083495

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01083495

Keywords

Search

Navigation