Representations of solvable Lie groups : basic theory and examples

著者

書誌事項

Representations of solvable Lie groups : basic theory and examples

Didier Arnal, Bradley Currey

（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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