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| Softcover ISBN: | 978-1-4704-7999-2 |
| Product Code: | GSM/64.S |
| List Price: | $89.00 |
| MAA Member Price: | $80.10 |
| AMS Member Price: | $71.20 |
| eBook ISBN: | 978-1-4704-1799-4 |
| Product Code: | GSM/64.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-7999-2 |
| eBook ISBN: | 978-1-4704-1799-4 |
| Product Code: | GSM/64.S.B |
| List Price: | $174.00 $131.50 |
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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 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.
ReadershipGraduate students and research mathematicians interested in representation theory.
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Table of Contents
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Chapters
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Chapter 1. Geometry of coadjoint orbits
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Chapter 2. Representations and orbits of the Heisenberg group
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Chapter 3. The orbit method for nilpotent Lie groups
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Chapter 4. Solvable Lie groups
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Chapter 5. Compact Lie groups
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Chapter 6. Miscellaneous
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Chapter 7. Abstract nonsense
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Chapter 8. Smooth manifolds
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Chapter 9. Lie groups and homogeneous manifolds
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Chapter 10. Elements of functional analysis
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Chapter 11. Representation theory
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Additional Material
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Reviews
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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
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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 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.
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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.
EMS Newsletter
