Representation Theory and Complex Analysis

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

  • Michael Cowling
  • Edward Frenkel
  • Masaki Kashiwara
  • Alain Valette
  • David A. VoganJr
  • Nolan R. Wallach
  • Enrico Casadio Tarabusi
  • Andrea D'Agnolo
  • Massimo Picardello

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

Table of contents

About this book

Introduction

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.

Keywords

Complex analysis Langlands correspondence Representation theory abstract harmonic analysis harmonic analysis quasi-equivariant D-modules semisimple Lie groups unitary representations

Authors and affiliations

  • Michael Cowling
    • 1
  • Edward Frenkel
    • 2
  • Masaki Kashiwara
    • 3
  • Alain Valette
    • 4
  • David A. VoganJr
    • 5
  • Nolan R. Wallach
    • 6
  1. 1.School of MathematicsUniversity of New South Wales2052Australia
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  3. 3.Research Institute for Mathematical SciencesKyoto University606-8502Japan
  4. 4.Institut de MathématiquesUniversity of Neuchâtel2009Switzerland
  5. 5.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  6. 6.Department of MathematicsUniversity of CaliforniaSan DiegoUSA

Editors and affiliations

  • Enrico Casadio Tarabusi
    • 1
  • Andrea D'Agnolo
    • 2
  • Massimo Picardello
    • 3
  1. 1.Dipartimento di Matematica “G. Castelnuovo”Sapienza Università di RomaItaly
  2. 2.Dipartimento di Matematica Pura ed ApplicataUniversità degli Studi di PadovaItaly
  3. 3.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”Italy

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-76892-0
  • Copyright Information Springer Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-76891-3
  • Online ISBN 978-3-540-76892-0
  • Series Print ISSN 0075-8434
  • About this book
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