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Lectures on the Orbit Method

A. A. Kirillov University of Pennsylvania, Philadelphia, PA
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Hardcover ISBN: 978-0-8218-3530-2
Product Code: GSM/64
List Price: $80.00 MAA Member Price:$72.00
AMS Member Price: $64.00 Electronic ISBN: 978-1-4704-1799-4 Product Code: GSM/64.E List Price:$75.00
MAA Member Price: $67.50 AMS Member Price:$60.00
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List Price: $120.00 MAA Member Price:$108.00
AMS Member Price: $96.00 Click above image for expanded view Lectures on the Orbit Method A. A. Kirillov University of Pennsylvania, Philadelphia, PA Available Formats:  Hardcover ISBN: 978-0-8218-3530-2 Product Code: GSM/64  List Price:$80.00 MAA Member Price: $72.00 AMS Member Price:$64.00
 Electronic ISBN: 978-1-4704-1799-4 Product Code: GSM/64.E
 List Price: $75.00 MAA Member Price:$67.50 AMS Member Price: $60.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$120.00 MAA Member Price: $108.00 AMS Member Price:$96.00
• Book Details

Volume: 642004; 408 pp
MSC: 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 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.

• 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

• Reviews

• 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.

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 642004; 408 pp
MSC: 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 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.

• 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 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.