Induced Representations of Locally Compact Groups

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Eberhard Kaniuth (Universität Paderborn, Germany) Keith F. Taylor (Dalhousie University, Nova Scotia)

Induced Representations of Locally Compact Groups

Eberhard Kaniuth (Universität Paderborn, Germany), Keith F. Taylor (Dalhousie University, Nova Scotia)

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English

Cambridge University Press
22 November 2012

Algebra; Groups & group theory; Algebraic topology

Series: Cambridge Tracts in Mathematics

The dual space of a locally compact group G consists of the equivalence classes of irreducible unitary representations of G. This book provides a comprehensive guide to the theory of induced representations and explains its use in describing the dual spaces for important classes of groups. It introduces various induction constructions and proves the core theorems on induced representations, including the fundamental imprimitivity theorem of Mackey and Blattner. An extensive introduction to Mackey analysis is applied to compute dual spaces for a wide variety of examples. Fell's contributions to understanding the natural topology on the dual are also presented. In the final two chapters, the theory is applied in a variety of settings including topological Frobenius properties and continuous wavelet transforms. This book will be useful to graduate students seeking to enter the area as well as experts who need the theory of unitary group representations in their research.

By: Eberhard Kaniuth (Universität Paderborn Germany), Keith F. Taylor (Dalhousie University, Nova Scotia)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 197
Dimensions: Height: 234mm, Width: 157mm, Spine: 22mm
Weight: 630g
ISBN: 9780521762267
ISBN 10: 052176226X
Series: Cambridge Tracts in Mathematics
Pages: 355
Publication Date: 22 November 2012
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Active

1. Basics; 2. Induced representations; 3. The imprimitivity theorem; 4. Mackey analysis; 5. Topologies on dual spaces; 6. Topological Frobenius properties; 7. Further applications; References; Index.

Eberhard Kaniuth is Professor Emeritus at the University of Paderborn, Germany. Keith F. Taylor is Associate Vice-President Academic and a Professor in the Department of Mathematics and Statistics at Dalhousie University, Nova Scotia.