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Look Inside Representations of Solvable Lie Groups

Representations of Solvable Lie Groups
Basic Theory and Examples

Part of New Mathematical Monographs

  • Publication planned for: June 2020
  • availability: Not yet published - available from June 2020
  • format: Hardback
  • isbn: 9781108428095

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  • 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.

    • Concrete and example-based exposition is accessible to advanced graduate students and non-specialists
    • Contains the first self-contained presentation of the Auslander–Kostant theory
    • Includes a new layer-wise description of the structure of the orbit space for any finite-dimensional linear solvable action, which has various potential applications
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    Product details

    • Publication planned for: June 2020
    • format: Hardback
    • isbn: 9781108428095
    • dimensions: 235 x 157 x 28 mm
    • weight: 0.76kg
    • availability: Not yet published - available from June 2020
  • Table of Contents

    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.

  • Authors

    Didier Arnal, Université de Bourgogne, France
    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.

    Bradley Currey, Saint Louis University, Missouri
    Bradley Currey III is a professor at Saint Louis University (SLU), Missouri. Formerly the Director of Graduate Studies in Mathematics at SLU, he has also served as a co-organizer in the Mathematics Research Communities program of the American Mathematical Society. Much of his recent research has explored the interplay of the theory of solvable Lie groups and applied harmonic analysis.

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