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Representation Theory and Complex Analysis

Lectures given at the C.I.M.E. Summer School held in Venice, Italy, June 10-17, 2004

  • Book
  • © 2008

Overview

Authors:
  1. Michael Cowling

    1. School of Mathematics, University of New South Wales, 2052, Australia

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  2. Edward Frenkel

    1. Department of Mathematics, University of California, Berkeley, USA

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  3. Masaki Kashiwara

    1. Research Institute for Mathematical Sciences, Kyoto University, 606-8502, Japan

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  4. Alain Valette

    1. Institut de Mathématiques, University of Neuchâtel, 2009, Switzerland

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  5. David A. Vogan

    1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

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  6. Nolan R. Wallach

    1. Department of Mathematics, University of California, San Diego, USA

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Editors:
  1. Enrico Casadio Tarabusi

    1. Dipartimento di Matematica “G. Castelnuovo”, Sapienza Università di Roma, Italy

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  2. Andrea D'Agnolo

    1. Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Italy

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  3. Massimo Picardello

    1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Italy

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1931)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XII
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  2. Applications of Representation Theory to Harmonic Analysis of Lie Groups (and Vice Versa)

    • Michael Cowling
    Pages 1-50

  3. Ramifications of the Geometric Langlands Program

    • Edward Frenkel
    Pages 51-135

  4. Equivariant Derived Category and Representation of Real Semisimple Lie Groups

    • Masaki Kashiwara
    Pages 137-234

  5. Amenability and Margulis Super-Rigidity

    • Alain Valette
    Pages 235-258

  6. Unitary Representations and Complex Analysis

    • David A. Vogan Jr
    Pages 259-344

  7. Quantum Computing and Entanglement for Mathematicians

    • Nolan R. Wallach
    Pages 345-376

  8. Back Matter

    Pages 377-388
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Keywords

About this book

Six leading experts lecture on a wide spectrum of recent results on the subject of the title, providing both a solid reference and deep insights on current research activity. Michael Cowling presents a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces. Alain Valette recalls the concept of amenability and shows how it is used in the proof of rigidity results for lattices of semisimple Lie groups. Edward Frenkel describes the geometric Langlands correspondence for complex algebraic curves, concentrating on the ramified case where a finite number of regular singular points is allowed. Masaki Kashiwara studies the relationship between the representation theory of real semisimple Lie groups and the geometry of the flag manifolds associated with the corresponding complex algebraic groups. David Vogan deals with the problem of getting unitary representations out of those arising from complex analysis, such as minimal globalizations realized on Dolbeault cohomology with compact support. Nolan Wallach illustrates how representation theory is related to quantum computing, focusing on the study of qubit entanglement.

Authors, Editors and Affiliations

  • Dipartimento di Matematica “G. Castelnuovo”, Sapienza Università di Roma, Italy

    Enrico Casadio Tarabusi

  • Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Italy

    Andrea D'Agnolo

  • Dipartimento di Matematica, Università di Roma “Tor Vergata”, Italy

    Massimo Picardello

  • School of Mathematics, University of New South Wales, 2052, Australia

    Michael Cowling

  • Department of Mathematics, University of California, Berkeley, USA

    Edward Frenkel

  • Research Institute for Mathematical Sciences, Kyoto University, 606-8502, Japan

    Masaki Kashiwara

  • Institut de Mathématiques, University of Neuchâtel, 2009, Switzerland

    Alain Valette

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

    David A. Vogan

  • Department of Mathematics, University of California, San Diego, USA

    Nolan R. Wallach

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