Unitary representations of groups, duals, and characters / Bachir Bekka, Pierre de la Harpe.

Format:

Book

Author/Creator:

Bekka, M. Bachir, author.

La Harpe, Pierre de, author.

Series:

Mathematical Surveys and Monographs

Mathematical Surveys and Monographs, 2331-7159 ; v. 250

Language:

English

Subjects (All):

Representations of groups.

Physical Description:

1 online resource (xi, 474 pages)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2020]

Language Note:

English

Summary:

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.

Contents:

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 and of LC groups, the Glimm theorem

Examples of primitive duals

Normal quasi-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.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-6287-7

OCLC:

1228043092