Lectures on the orbit method / A. A. Kirillov.

Format:

Book

Author/Creator:

Kirillov, A. A. (Aleksandr Aleksandrovich), 1936- author.

Series:

Graduate studies in mathematics ; Volume 64.

Graduate Studies in Mathematics ; Volume 64

Language:

English

Subjects (All):

Orbit method.

Lie groups.

Physical Description:

1 online resource (408 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2004.

Language Note:

English

Summary:

Isaac Newton encrypted his discoveries in analysis in the form of an anagram, which 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.

Contents:

""Cover""; ""Title page""; ""Contents""; ""Preface""; ""Introduction""; ""Geometry of coadjoint orbits""; ""Representations and orbits of the Heisenberg group""; ""The orbit method for nilpotent Lie groups""; ""Solvable Lie groups""; ""Compact Lie groups""; ""Miscellaneous""; ""Abstract nonsense""; ""Smooth manifolds""; ""Lie groups and homogeneous manifolds""; ""Elements of functional analysis""; ""Representation theory""; ""References""; ""Index""; ""Back Cover""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-1799-5

OCLC:

922965233