Unitary representations of groups, duals, and characters
Author(s)
Bibliographic Information
Unitary representations of groups, duals, and characters
(Mathematical surveys and monographs, v. 250)
American Mathematical Society, c2020
- : pbk
Available at 25 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbkS||MSM||250200040924400
Note
Includes bibliographical references (p. 447-461) and indexes
Description and Table of Contents
Description
Unitary representations of groups play an important role in many subjects, including number theory, geometry, probability theory, partial differential equations, and quantum mechanics. This monograph focuses on dual spaces associated to a group, which are spaces of building blocks of general unitary representations. Special attention is paid to discrete groups for which the unitary dual, the most common dual space, has proven to be not useful in general and for which other duals spaces have to be considered, such as the primitive dual, the normal quasi-dual, or spaces of characters. The book offers a detailed exposition of these alternative dual spaces and covers the basic facts about unitary representations and operator algebras needed for their study. Complete and elementary proofs are provided for most of the fundamental results that up to now have been accessible only in original papers and appear here for the first time in textbook form. A special feature of this monograph is that the theory is systematically illustrated by a family of examples of discrete groups for which the various dual spaces are discussed in great detail: infinite dihedral group, Heisenberg groups, affine groups of fields, solvable Baumslag-Solitar group, lamplighter group, and general and special linear groups. The book will appeal to graduate students who wish to learn the basics facts of an important topic and provides a useful resource for researchers from a variety of areas. The only prerequisites are a basic background in group theory, measure theory, and operator algebras.
Table of Contents
Introduction
Unitary dual and primitive dual
Representations of locally compact abelian groups
Examples of irreducible representations
Finite-dimensional irreducible representations
Describing all irreducible representations of some semi-direct products
Types for representations, quasi-duals, groups of type I
Non type I groups
Representations of C*-algebras of LC groups, the Glimm Theorem
Examples of primitive duals
Normal qluasi-dual and characters
Finite characters and Thoma's dual
Examples of Thoma's duals
The group measure space construction
Construction of factor representations for some semi-direct products
Separating families of finite type representations
Appendix
Bibliography
Notation index
Index.
by "Nielsen BookData"