Hardcover ISBN:  9780821835302 
Product Code:  GSM/64 
List Price:  $80.00 
MAA Member Price:  $72.00 
AMS Member Price:  $64.00 
Electronic ISBN:  9781470417994 
Product Code:  GSM/64.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $60.00 

Book DetailsGraduate Studies in MathematicsVolume: 64; 2004; 408 ppMSC: Primary 22;
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 nonexperts and gives the first systematic, detailed, and selfcontained 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 nonexperts and a reference book for research mathematicians and mathematical physicists.ReadershipGraduate students and research mathematicians interested in representation theory.

Table of Contents

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


Additional Material

Reviews

The book offers a nicely written, systematic and readable 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


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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 nonexperts and gives the first systematic, detailed, and selfcontained 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 nonexperts and a reference book for research mathematicians and mathematical physicists.
Graduate students and research mathematicians interested in representation theory.

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

The book offers a nicely written, systematic and readable 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