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Lectures on the Orbit Method
A. A. Kirillov, University of Pennsylvania, Philadelphia, PA

Graduate Studies in Mathematics
2004; 408 pp; hardcover
Volume: 64
ISBN-10: 0-8218-3530-0
ISBN-13: 978-0-8218-3530-2
List Price: US$75
Member Price: US$60
Order Code: GSM/64
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See also:

Representations of Semisimple Lie Algebras in the BGG Category \(\mathscr {O}\) - James E Humphreys

Introduction to Representation Theory - Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob and Elena Yudovina

Isaac Newton encrypted his discoveries in analysis in the form of an anagram that deciphers to the sentence, "It is worthwhile to solve differential equations". Accordingly, one can express the main idea behind the orbit method by saying "It is worthwhile to study coadjoint orbits".

The orbit method was introduced by the author, A. A. Kirillov, in the 1960s and remains a useful and powerful tool in areas such as Lie theory, group representations, integrable systems, complex and symplectic geometry, and mathematical physics. This book describes the essence of the orbit method for non-experts and gives the first systematic, detailed, and self-contained exposition of the method. It starts with a convenient "User's Guide" and contains numerous examples. It can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.


Graduate students and research mathematicians interested in representation theory.


"The book offers a nicely written, systematic and read-able description of the orbit method for various classes of Lie groups. ...should be on the shelves of mathematicians and theoretical physicists using representation theory in their work."

-- EMS Newsletter

Table of Contents

  • Geometry of coadjoint orbits
  • Representations and orbits of the Heisenberg group
  • The orbit method for nilpotent Lie groups
  • Solvable Lie groups
  • Compact Lie groups
  • Miscellaneous
  • Abstract nonsense
  • Smooth manifolds
  • Lie groups and homogeneous manifolds
  • Elements of functional analysis
  • Representation theory
  • References
  • Index
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