Skip to main content
SpringerLink
Log in

Analysis in matrix space and Speh's representations

  • Published:
Inventiones mathematicae 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

References

  • [B] Blattner, R.J.: On induced representations II: infinitesimal induction. Am. J. Math.83, 499–512 (1961)

    Google Scholar 

  • [BSS] Barbasch, D., Sahi, S., Speh, B.: Degenerate series representations forGL(2n, R) and Fourier Analysis. In: Indecomposable representations and Physics. Conference, Rome 1988 (to appear)

  • [GG] Gelfand, I.M., Graev, I.: Unitary representations of the real unimodular group. Transl. Am. Math. Soc.2, 147–205 (1956)

    Google Scholar 

  • [GGV] Gelfand, I.M., Graev, I., Vilenkin, N.: Generalized Functions V: Integral Geometry and Representation Theory. New York: Academic Press 1966

    Google Scholar 

  • [H] Harish-Chandra: Representations of a semisimple Lie group on a Banach space I. Trans. Am. Math. Soc.75, 185–243 (1953)

    Google Scholar 

  • [He] Herz, C.S.: Bessel functions of matrix argument. Ann. Math.61, 474–523 (1955)

    Google Scholar 

  • [Hu] Hua, L.K.: Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains. Transl. Math. Monogr. vol. 6, Amer. Math. Soc., 1963

  • [K] Kirillov, A.A.: Infinite dimensional representations of the general linear group. Sov. Math. Dokl.3, 652–655 (1962)

    Google Scholar 

  • [S1] Sahi, S.: On Kirillov's Conjecture for archimedean fields. Compos. Math.72, 67–86 (1989)

    Google Scholar 

  • [S2] Sahi, S.: A simple construction of Stein's complementary series. Proc. Am. Math. Soc.108 (1), 257–266 (1990)

    Google Scholar 

  • [Sp] Speh, B.: Unitary representations ofSL(n, R) and the cohomology of congruence subgroups. In: non-commutative Harmonic Analysis and Lie Groups, (Lect. Notes Math., vol. 880, pp. 483–505). Berlin-Heidelberg-New York: Springer 1981

    Google Scholar 

  • [St] Stein, E.: Analysis in matrix space and some new representations ofSL(n, C). Ann. Math.86, 461–490 (1967)

    Google Scholar 

  • [V1] Vogan, D.: Representations of Real Reductive Lie groups. Boston-Basel-Stuttgart: Birkhäuser 1981

    Google Scholar 

  • [V2] Vogan, D.: The unitary dual ofGL(n) over an archimedean field. Invent. Math.83, 449–505 (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA

    Siddhartha Sahi & Elias M. Stein

Authors
  1. Siddhartha Sahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elias M. Stein
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The authors were supported in part by NSF grants at Princeton University and at MSRI, Berkeley

Oblatum 16-VI-1989

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sahi, S., Stein, E.M. Analysis in matrix space and Speh's representations. Invent Math 101, 379–393 (1990). https://doi.org/10.1007/BF01231507

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01231507

Keywords

Search

Navigation