Representations of Solvable Lie Groups
Basic Theory and Examples

A complete and self-contained account of the basic theory of unitary group representations for graduate students and researchers.

Didier Arnal (Author), Bradley Currey (Author)

9781108428095, Cambridge University Press

Hardback, published 16 April 2020

478 pages
23.5 x 15.7 x 2.8 cm, 0.76 kg

'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.' Béchir Dali, zbMATH

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.

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.

Subject Areas: Functional analysis & transforms [PBKF], Algebra [PBF]