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Books > Science & Mathematics > Mathematics > Algebra
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Unitary Representations of Groups, Duals, and Characters (Paperback)
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Unitary Representations of Groups, Duals, and Characters (Paperback)
Series: Mathematical Surveys and Monographs
Expected to ship within 12 - 17 working days
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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.
General
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