Lectures on the Orbit Method  - Kirillov

Lectures on the Orbit Method


Yayınevi: American Mathematical Society AMS

Yayın tarihi: 08/2004

ISBN: 9780821835302

Ciltli | İngilizce | 432 Sayfa |

Tür: Matematik-İstatistik

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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. Ch. 1 Geometry of coadjoint orbits 1
Ch. 2 Representations and orbits of the Heisenberg group 31
Ch. 3 The orbit method for Nilpotent Lie groups 71
Ch. 4 Solvable Lie groups 109
Ch. 5 Compact Lie groups 135
Ch. 6 Miscellaneous 179
App. I Abstract nonsense 207
App. II Smooth manifolds 227
App. III Lie groups and homogeneous manifolds 269
App. IV Elements of functional analysis 333
App. V Representation theory 357

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