Isaac Newton encrypted his discoveries in analysis in the form of an anagram, which 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.
Rezensionen / Stimmen
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
Reihe
Sprache
Verlagsort
Zielgruppe
ISBN-13
978-1-4704-7999-2 (9781470479992)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Klassifikation
A. A. Kirillov, University of Pennsylvania, Philadelphia, PA.
Chapters
Chapter 1. Geometry of coadjoint orbits
Chapter 2. Representations and orbits of the Heisenberg group
Chapter 3. The orbit method for nilpotent Lie groups
Chapter 4. Solvable Lie groups
Chapter 5. Compact Lie groups
Chapter 6. Miscellaneous
Chapter 7. Abstract nonsense
Chapter 8. Smooth manifolds
Chapter 9. Lie groups and homogeneous manifolds
Chapter 10. Elements of functional analysis
Chapter 11. Representation theory
