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The Weil representation, Maslov index and Theta series

  • Book
  • © 1980

Overview

Authors:
  1. Gérard Lion

    1. X U.E.R. de Sciences Economiques, Université de Paris, Nanterre, France

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    You can also search for this author in PubMed   Google Scholar

  2. Michèle Vergne

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

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Progress in Mathematics (PM, volume 6)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-viii
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  2. The Shale-Weil representation and the Maslov Index

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Gérard Lion, Michèle Vergne
      Pages 3-6

    3. Symplectic vector spaces and the Heisenberg Lie algebra

      • Gérard Lion, Michèle Vergne
      Pages 7-11

    4. The Heisenberg group and the Schrödinger representation

      • Gérard Lion, Michèle Vergne
      Pages 12-15

    5. The Weyl transform and the Stone-Von Neumann theorem

      • Gérard Lion, Michèle Vergne
      Pages 16-29

    6. Fourier transforms and intertwining operators

      • Gérard Lion, Michèle Vergne
      Pages 30-38

    7. Maslov index

      • Gérard Lion, Michèle Vergne
      Pages 39-46

    8. The cocycle of the Shale-Weil representation and the Maslov index

      • Gérard Lion, Michèle Vergne
      Pages 47-63

    9. Oriented Lagrangian planes and the metaplectic group

      • Gérard Lion, Michèle Vergne
      Pages 64-72

    10. The universal covering group of SL(2,ℝ)

      • Gérard Lion, Michèle Vergne
      Pages 73-83

    11. The universal covering group of the symplectic group

      • Gérard Lion, Michèle Vergne
      Pages 84-103

  3. The Shale-Weil representation. θ-series and correspondences

    1. Front Matter

      Pages 121-121
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    2. Introduction

      • Gérard Lion, Michèle Vergne
      Pages 123-137

    3. Lattices and representations of the Heisenberg group

      • Gérard Lion, Michèle Vergne
      Pages 138-148

    4. The multiplier of θ

      • Gérard Lion, Michèle Vergne
      Pages 149-176

    5. Modular forms on the upper half-plane

      • Gérard Lion, Michèle Vergne
      Pages 177-196

    6. Modular forms of weight 1/2

      • Gérard Lion, Michèle Vergne
      Pages 197-208

    7. The Shale-Weil representation associated to a quadratic form

      • Gérard Lion, Michèle Vergne
      Pages 209-246

    8. θ-Series Associated to Quadratic forms

      • Gérard Lion, Michèle Vergne
      Pages 247-267
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Keywords

About this book

* A collection of research-oriented monographs, reports, notes arising from lectures or seminars

* Quickly published concurrent with research

* Easily accessible through international distribution facilities

* Reasonably priced

* Reporting research developments combining original results with an expository treatment of the particular subject area

* A contribution to the international scientific community: for colleagues and for graduate students who are seeking current information and directions in their graduate and post-graduate work

Authors and Affiliations

  • X U.E.R. de Sciences Economiques, Université de Paris, Nanterre, France

    Gérard Lion

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

    Michèle Vergne

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