Compact Lie Groups and Their Representations

D. P. Zelobenko

ISBN 10: 0821815903 / ISBN 13: 9780821815908

Published by American Mathematical Society, US, 1973

About this Item

The contents of this volume are somewhat different from the traditional connotations of the title. First, the author, bearing in mind the needs of the physicist, has tried to make the exposition as elementary as possible. The need for an elementary exposition has influenced the distribution of the material; the book is divided into three largely independent parts, arranged in order of increasing difficulty. Besides compact Lie groups, groups with other topological structure ('similar' to compact groups in some sense) are considered.Prominent among these are reductive complex Lie groups (including semisimple groups), obtained from compact Lie groups by analytic continuation, and also their real forms (reductive real Lie groups). The theory of finite-dimensional representation for these classes of groups is developed, striving whenever possible to emphasize the 'compact origin' of these representations, i.e. their analytic relationship to representations of compact Lie groups. Also studied are infinite-dimensional representations of semisimple complex Lie algebras. Some aspects of the theory of infinite-dimensional representations of Lie groups are presented in a brief survey.

Seller Inventory # LU-9780821815908

Bibliographic Details

• Title: Compact Lie Groups and Their Representations
• Publisher: American Mathematical Society, US
• Publication Date: 1973
• Language: English
• ISBN 10: 0821815903
• ISBN 13: 9780821815908
• Binding: Paperback
• Condition: New
• Dimensions: 17.78W x 2.54H x 26.04D centimeters 17.78 centimeters width by 2.54 centimeters height by 26.04 centimeters depth
• Weight: 840 grams

About this title

Synopsis

The contents of this volume are somewhat different from the traditional connotations of the title. First, the author, bearing in mind the needs of the physicist, has tried to make the exposition as elementary as possible. The need for an elementary exposition has influenced the distribution of the material; the book is divided into three largely independent parts, arranged in order of increasing difficulty. Besides compact Lie groups, groups with other topological structure (``similar'' to compact groups in some sense) are considered. Prominent among these are reductive complex Lie groups (including semisimple groups), obtained from compact Lie groups by analytic continuation, and also their real forms (reductive real Lie groups). The theory of finite-dimensional representation for these classes of groups is developed, striving whenever possible to emphasize the ``compact origin'' of these representations, i.e. their analytic relationship to representations of compact Lie groups. Also studied are infinite-dimensional representations of semisimple complex Lie algebras. Some aspects of the theory of infinite-dimensional representations of Lie groups are presented in a brief survey.

Language Notes

Text: English, Russian (translation)