Representations of solvable Lie groups : basic theory and examples
著者
書誌事項
Representations of solvable Lie groups : basic theory and examples
（New mathematical monographs, 39）
Cambridge University Press, 2020
- : hardback
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注記
Includes bibliographical references (p. 440-444) and index
内容説明・目次
内容説明
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.
目次
- 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.
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