Representations of Solvable Lie Groups

Basic Theory and Examples

Didier Arnal, Bradley Currey

• Publisher: Cambridge University Press
• Year: 2020
• Print ISBN: 9781108428095
• eBook ISBN: 9781108651936
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

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.

Table of contents

• Cover
• Half-title
• Series information
• Title page
• Copyright information
• Dedication
• Contents
• Preface
• 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