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Introduction to Orthogonal, Symplectic and Unitary Representations of Finite Groups

Carl R. Riehm McMaster University, Hamilton, ON, Canada and The Fields Institute, Toronto, ON, Canada
A co-publication of the AMS and Fields Institute
Available Formats:
Hardcover ISBN: 978-0-8218-4271-3
Product Code: FIM/28
List Price: $111.00 MAA Member Price:$99.90
AMS Member Price: $88.80 Electronic ISBN: 978-1-4704-1791-8 Product Code: FIM/28.E List Price:$104.00
MAA Member Price: $93.60 AMS Member Price:$83.20
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List Price: $166.50 MAA Member Price:$149.85
AMS Member Price: $133.20 Click above image for expanded view Introduction to Orthogonal, Symplectic and Unitary Representations of Finite Groups Carl R. Riehm McMaster University, Hamilton, ON, Canada and The Fields Institute, Toronto, ON, Canada A co-publication of the AMS and Fields Institute Available Formats:  Hardcover ISBN: 978-0-8218-4271-3 Product Code: FIM/28  List Price:$111.00 MAA Member Price: $99.90 AMS Member Price:$88.80
 Electronic ISBN: 978-1-4704-1791-8 Product Code: FIM/28.E
 List Price: $104.00 MAA Member Price:$93.60 AMS Member Price: $83.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$166.50 MAA Member Price: $149.85 AMS Member Price:$133.20
• Book Details

Fields Institute Monographs
Volume: 282011; 291 pp
MSC: Primary 20; 11; 16;

Orthogonal, symplectic and unitary representations of finite groups lie at the crossroads of two more traditional subjects of mathematics—linear representations of finite groups, and the theory of quadratic, skew symmetric and Hermitian forms—and thus inherit some of the characteristics of both.

This book is written as an introduction to the subject and not as an encyclopaedic reference text. The principal goal is an exposition of the known results on the equivalence theory, and related matters such as the Witt and Witt-Grothendieck groups, over the “classical” fields—algebraically closed, real closed, finite, local and global. A detailed exposition of the background material needed is given in the first chapter.

It was A. Fröhlich who first gave a systematic organization of this subject, in a series of papers beginning in 1969. His paper Orthogonal and symplectic representations of groups represents the culmination of his published work on orthogonal and symplectic representations. The author has included most of the work from that paper, extending it to include unitary representations, and also providing new approaches, such as the use of the equivariant Brauer-Wall group in describing the principal invariants of orthogonal representations and their interplay with each other.

Graduate students and research mathematicians interested in the representations of finite groups, surgery theory, or equivariant superalgebras.

• Chapters
• Chapter 1. Background material
• Chapter 2. Isometry representations of finite groups
• Chapter 3. Hermitian forms over semisimple algebras
• Chapter 4. Equivariant Witt-Grothendieck and Witt groups
• Chapter 5. Representations over finite, local and global fields
• Chapter 6. Fröhlich’s invariant, Clifford algebras and the equivariant Brauer-Wall group

• Reviews

• This book is a most welcome introduction to this wonderful subject with deep roots in two classical areas of mathematics, collecting in one place the most recent developments. It can be profitably read by anyone interested with a basic background on representation theory and quadratic forms.

MAA Reviews
• Request Review Copy
Volume: 282011; 291 pp
MSC: Primary 20; 11; 16;

Orthogonal, symplectic and unitary representations of finite groups lie at the crossroads of two more traditional subjects of mathematics—linear representations of finite groups, and the theory of quadratic, skew symmetric and Hermitian forms—and thus inherit some of the characteristics of both.

This book is written as an introduction to the subject and not as an encyclopaedic reference text. The principal goal is an exposition of the known results on the equivalence theory, and related matters such as the Witt and Witt-Grothendieck groups, over the “classical” fields—algebraically closed, real closed, finite, local and global. A detailed exposition of the background material needed is given in the first chapter.

It was A. Fröhlich who first gave a systematic organization of this subject, in a series of papers beginning in 1969. His paper Orthogonal and symplectic representations of groups represents the culmination of his published work on orthogonal and symplectic representations. The author has included most of the work from that paper, extending it to include unitary representations, and also providing new approaches, such as the use of the equivariant Brauer-Wall group in describing the principal invariants of orthogonal representations and their interplay with each other.

Graduate students and research mathematicians interested in the representations of finite groups, surgery theory, or equivariant superalgebras.

• Chapters
• Chapter 1. Background material
• Chapter 2. Isometry representations of finite groups
• Chapter 3. Hermitian forms over semisimple algebras
• Chapter 4. Equivariant Witt-Grothendieck and Witt groups
• Chapter 5. Representations over finite, local and global fields
• Chapter 6. Fröhlich’s invariant, Clifford algebras and the equivariant Brauer-Wall group
• This book is a most welcome introduction to this wonderful subject with deep roots in two classical areas of mathematics, collecting in one place the most recent developments. It can be profitably read by anyone interested with a basic background on representation theory and quadratic forms.

MAA Reviews
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