**Graduate Studies in Mathematics**

Volume: 64;
2004;
408 pp;
Hardcover

MSC: Primary 22;

Print ISBN: 978-0-8218-3530-2

Product Code: GSM/64

List Price: $75.00

Individual Member Price: $60.00

**Electronic ISBN: 978-1-4704-1799-4
Product Code: GSM/64.E**

List Price: $75.00

Individual Member Price: $60.00

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#### Supplemental Materials

# Lectures on the Orbit Method

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*A. A. Kirillov*

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.

#### Table of Contents

# Table of Contents

## Lectures on the Orbit Method

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xv16 free
- Introduction xvii18 free
- Geometry of coadjoint orbits 122 free
- Representations and orbits of the Heisenberg group 3152
- The orbit method for nilpotent Lie groups 7192
- Solvable Lie groups 109130
- Compact Lie groups 135156
- Miscellaneous 179200
- Abstract nonsense 207228
- Smooth manifolds 227248
- Lie groups and homogeneous manifolds 269290
- Elements of functional analysis 333354
- Representation theory 357378
- References 395416
- Index 403424 free
- Back Cover Back Cover1434

#### Readership

Graduate students and research mathematicians interested in 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.

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