© 2003

The Orbit Method in Geometry and Physics

In Honor of A.A. Kirillov

  • Christian Duval
  • Valentin Ovsienko
  • Laurent Guieu

Part of the Progress in Mathematics book series (PM, volume 213)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. A. Alekseev, F. Petrov
    Pages 1-7
  3. Jacques Alev, Daniel R. Farkas
    Pages 9-28
  4. Vladimir Baranovsky, Sam Evens, Victor Ginzburg
    Pages 29-48
  5. Vassily Gorbounov, Fyodor Malikov, Vadim Schechtman
    Pages 73-100
  6. Pavel Grozman, Dimitry Leites, Irina Shchepochkina
    Pages 101-146
  7. Anthony Joseph, Anna Melnikov
    Pages 165-196
  8. A. A. Kirillov
    Pages 243-258
  9. Bertram Kostant, Peter W. Michor
    Pages 259-296
  10. Andrei Okounkov
    Pages 329-347
  11. W. Rossmann
    Pages 395-419
  12. Back Matter
    Pages 473-474

About this book


The volume is dedicated to AA. Kirillov and emerged from an international con­ ference which was held in Luminy, Marseille, in December 2000, on the occasion 6 of Alexandre Alexandrovitch's 2 th birthday. The conference was devoted to the orbit method in representation theory, an important subject that influenced the de­ velopment of mathematics in the second half of the XXth century. Among the famous names related to this branch of mathematics, the name of AA Kirillov certainly holds a distinguished place, as the inventor and founder of the orbit method. The research articles in this volume are an outgrowth of the Kirillov Fest and they illustrate the most recent achievements in the orbit method and other areas closely related to the scientific interests of AA Kirillov. The orbit method has come to mean a method for obtaining the representations of Lie groups. It was successfully applied by Kirillov to obtain the unitary rep­ resentation theory of nilpotent Lie groups, and at the end of this famous 1962 paper, it was suggested that the method may be applicable to other Lie groups as well. Over the years, the orbit method has helped to link harmonic analysis (the theory of unitary representations of Lie groups) with differential geometry (the symplectic geometry of homogeneous spaces). This theory reinvigorated many classical domains of mathematics, such as representation theory, integrable sys­ tems, complex algebraic geometry. It is now a useful and powerful tool in all of these areas.


Lie algebra Lie groups Representation theory differential geometry geometrical quantization manifold mathematical physics symplectic geometry

Editors and affiliations

  • Christian Duval
    • 1
  • Valentin Ovsienko
    • 2
  • Laurent Guieu
    • 3
  1. 1.Centre de Physique Théorique CNRSCampus de LuminyMarseille Cedex 9France
  2. 2.Institut Girard DesarguesUniversité Claude Bernard Lyon 1Villeurbanne CedexFrance
  3. 3.Département des Sciences MathématiquesUniversité Montpellier IIMontpelier Cedex 5France

Bibliographic information


"…the volume might be useful to a large number of potential readers interested in various fields, like representation theory of Lie groups, symplectic geometry, differential equations, combinatorics, etc. It is noteworthy that the history of mathematics can also be added to this list of topics, due to the nice article authored by J. Dixmier."

—Romanian Journal of Pure and Appl. Math.