Representations of Solvable Lie Groups
Basic Theory and Examples
Published on 16. April 2020
Book
Hardback
478 pages
978-1-108-42809-5 (ISBN)
Description
The theory of unitary group representations began with finite groups, and blossomed in the twentieth century both as a natural abstraction of classical harmonic analysis, and as a tool for understanding various physical phenomena. Combining basic theory and new results, this monograph is a fresh and self-contained exposition of group representations and harmonic analysis on solvable Lie groups. Covering a range of topics from stratification methods for linear solvable actions in a finite-dimensional vector space, to complete proofs of essential elements of Mackey theory and a unified development of the main features of the orbit method for solvable Lie groups, the authors provide both well-known and new examples, with a focus on those relevant to contemporary applications. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers.
Reviews / Votes
'There is ... the included background material on Lie theory, and there are also quite a lot of examples provided. Aspiring researchers in this area will likely find these features helpful, both aspiring and current researchers should also appreciate the wealth of material found here, as well as the extensive (five page, 92 entries) bibliography.' Mark Hunacek, MAA Reviews '... embeddings into matrix algebras and unitary representations are both possible and useful, and they are given a central role in this book.' M. Bona, Choice 'Throughout the book, the authors carefully explain the theory step by step and provide many concrete examples with computations which help the readers to understand. This book is a valuable exposition and an excellent research guide for the basic representation theory of solvable Lie groups for graduate students and researchers.' Junko Inoue, MathSciNet 'This monograph is a summary of a long career and experience of two great experts in their domain. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers. The concrete and example-based exposition is accessible to advanced graduate students and non-specialists.' Bechir Dali, zbMATHMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 32 mm
Weight
899 gr
ISBN-13
978-1-108-42809-5 (9781108428095)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
E-Book
04/2020
Cambridge University Press
€118.99
Available for download
E-Book
04/2020
Cambridge University Press
€133.99
Available for download
Persons
Didier Arnal is Emeritus Professor at the University of Burgundy and previously was Director of the Burgundy Mathematics Institute. He instituted and has worked over the past fifteen years on a cooperation project between France and Tunisia. He has authored papers on a diverse range of topics including deformation quantization, harmonic analysis, and algebraic structures.
Content
1. Basic theory of solvable Lie algebras and Lie groups; 2. Stratification of an orbit space; 3. Unitary representations; 4. Coadjoint orbits and polarizations; 5. Irreducible unitary representations; 6. Plancherel formula and related topics; List of notations; Bibliography; Index.