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Representation Theory, Complex Analysis, and Integral Geometry pp 133–183Cite as

Stein–Sahi Complementary Series and Their Degenerations

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Abstract

The paper is an introduction to the Stein–Sahi complementary series and to unipotent representations. We also discuss some open problems related to these objects. For the sake of simplicity, we consider only the groups U(n, n).

Keywords

  • Unitary representations
  • Complementary series
  • Symmetric spaces
  • Non-commutative harmonic analysis
  • Classical groups
  • Unitary group
  • Highest weight representations
  • Unipotent representations

Mathematics Subject Classification (2010):42B35, 22D10

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Author information

Authors and Affiliations

  1. Mathematical Department, University of Vienna, Nordbergsrasse 15, Vienna, Austria

    Yuri A. Neretin

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

    Yuri A. Neretin

  3. MechMath Department, Moscow State University, Moscow, Russia

    Yuri A. Neretin

Authors
  1. Yuri A. Neretin
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Editor information

Editors and Affiliations

  1. , Institut für Analysis, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany

    Bernhard Krötz

  2. , Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 3200, Israel

    Omer Offen

  3. , Department of Mathematics, Ben-Gurion University of the Negev, Be'er Sheva, 84105, Israel

    Eitan Sayag

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Neretin, Y.A. (2012). Stein–Sahi Complementary Series and Their Degenerations. In: Krötz, B., Offen, O., Sayag, E. (eds) Representation Theory, Complex Analysis, and Integral Geometry. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4817-6_7

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